diff --git "a/cpp-compiled/sources/double-conversion/cached-powers.cc.ii" "b/cpp-compiled/sources/double-conversion/cached-powers.cc.ii"
new file mode 100644--- /dev/null
+++ "b/cpp-compiled/sources/double-conversion/cached-powers.cc.ii"
@@ -0,0 +1,22156 @@
+# 0 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+# 1 "/tmp/tmpl_i20ey9/double-conversion/build//"
+# 0 "<built-in>"
+# 0 "<command-line>"
+# 1 "/usr/include/stdc-predef.h" 1 3 4
+# 0 "<command-line>" 2
+# 1 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+# 28 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+# 1 "/usr/include/c++/13/climits" 1 3
+# 39 "/usr/include/c++/13/climits" 3
+       
+# 40 "/usr/include/c++/13/climits" 3
+
+# 1 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 1 3
+# 306 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+
+# 306 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+namespace std
+{
+  typedef long unsigned int size_t;
+  typedef long int ptrdiff_t;
+
+
+  typedef decltype(nullptr) nullptr_t;
+
+
+#pragma GCC visibility push(default)
+
+
+  extern "C++" __attribute__ ((__noreturn__, __always_inline__))
+  inline void __terminate() noexcept
+  {
+    void terminate() noexcept __attribute__ ((__noreturn__));
+    terminate();
+  }
+#pragma GCC visibility pop
+}
+# 339 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+namespace std
+{
+  inline namespace __cxx11 __attribute__((__abi_tag__ ("cxx11"))) { }
+}
+namespace __gnu_cxx
+{
+  inline namespace __cxx11 __attribute__((__abi_tag__ ("cxx11"))) { }
+}
+# 532 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+namespace std
+{
+#pragma GCC visibility push(default)
+
+
+
+
+  constexpr inline bool
+  __is_constant_evaluated() noexcept
+  {
+
+
+
+
+
+    return __builtin_is_constant_evaluated();
+
+
+
+  }
+#pragma GCC visibility pop
+}
+# 679 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+# 1 "/usr/include/aarch64-linux-gnu/c++/13/bits/os_defines.h" 1 3
+# 39 "/usr/include/aarch64-linux-gnu/c++/13/bits/os_defines.h" 3
+# 1 "/usr/include/features.h" 1 3 4
+# 394 "/usr/include/features.h" 3 4
+# 1 "/usr/include/features-time64.h" 1 3 4
+# 20 "/usr/include/features-time64.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 21 "/usr/include/features-time64.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/timesize.h" 1 3 4
+# 22 "/usr/include/features-time64.h" 2 3 4
+# 395 "/usr/include/features.h" 2 3 4
+# 502 "/usr/include/features.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 1 3 4
+# 576 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 577 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
+# 578 "/usr/include/aarch64-linux-gnu/sys/cdefs.h" 2 3 4
+# 503 "/usr/include/features.h" 2 3 4
+# 526 "/usr/include/features.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 1 3 4
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 6 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 2 3 4
+
+
+# 1 "/usr/include/aarch64-linux-gnu/gnu/stubs-lp64.h" 1 3 4
+# 9 "/usr/include/aarch64-linux-gnu/gnu/stubs.h" 2 3 4
+# 527 "/usr/include/features.h" 2 3 4
+# 40 "/usr/include/aarch64-linux-gnu/c++/13/bits/os_defines.h" 2 3
+# 680 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 2 3
+
+
+# 1 "/usr/include/aarch64-linux-gnu/c++/13/bits/cpu_defines.h" 1 3
+# 683 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 2 3
+# 882 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 3
+# 1 "/usr/include/c++/13/pstl/pstl_config.h" 1 3
+# 883 "/usr/include/aarch64-linux-gnu/c++/13/bits/c++config.h" 2 3
+# 42 "/usr/include/c++/13/climits" 2 3
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 1 3 4
+# 34 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 3 4
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/syslimits.h" 1 3 4
+
+
+
+
+
+
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 1 3 4
+# 205 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 3 4
+# 1 "/usr/include/limits.h" 1 3 4
+# 26 "/usr/include/limits.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
+# 27 "/usr/include/limits.h" 2 3 4
+# 195 "/usr/include/limits.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 28 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 2 3 4
+# 161 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 1 3 4
+# 38 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 3 4
+# 1 "/usr/include/linux/limits.h" 1 3 4
+# 39 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 2 3 4
+# 81 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/pthread_stack_min-dynamic.h" 1 3 4
+# 23 "/usr/include/aarch64-linux-gnu/bits/pthread_stack_min-dynamic.h" 3 4
+extern "C" {
+extern long int __sysconf (int __name) noexcept (true);
+}
+# 82 "/usr/include/aarch64-linux-gnu/bits/local_lim.h" 2 3 4
+# 162 "/usr/include/aarch64-linux-gnu/bits/posix1_lim.h" 2 3 4
+# 196 "/usr/include/limits.h" 2 3 4
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/posix2_lim.h" 1 3 4
+# 200 "/usr/include/limits.h" 2 3 4
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 1 3 4
+# 64 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/uio_lim.h" 1 3 4
+# 65 "/usr/include/aarch64-linux-gnu/bits/xopen_lim.h" 2 3 4
+# 204 "/usr/include/limits.h" 2 3 4
+# 206 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 2 3 4
+# 8 "/usr/lib/gcc/aarch64-linux-gnu/13/include/syslimits.h" 2 3 4
+# 35 "/usr/lib/gcc/aarch64-linux-gnu/13/include/limits.h" 2 3 4
+# 43 "/usr/include/c++/13/climits" 2 3
+# 29 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 2
+# 1 "/usr/include/c++/13/cmath" 1 3
+# 39 "/usr/include/c++/13/cmath" 3
+       
+# 40 "/usr/include/c++/13/cmath" 3
+
+# 1 "/usr/include/c++/13/bits/requires_hosted.h" 1 3
+# 42 "/usr/include/c++/13/cmath" 2 3
+
+
+# 1 "/usr/include/c++/13/bits/cpp_type_traits.h" 1 3
+# 35 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+       
+# 36 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+# 67 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+extern "C++" {
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  struct __true_type { };
+  struct __false_type { };
+
+  template<bool>
+    struct __truth_type
+    { typedef __false_type __type; };
+
+  template<>
+    struct __truth_type<true>
+    { typedef __true_type __type; };
+
+
+
+  template<class _Sp, class _Tp>
+    struct __traitor
+    {
+      enum { __value = bool(_Sp::__value) || bool(_Tp::__value) };
+      typedef typename __truth_type<__value>::__type __type;
+    };
+
+
+  template<typename, typename>
+    struct __are_same
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+  template<typename _Tp>
+    struct __are_same<_Tp, _Tp>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  template<typename _Tp>
+    struct __is_void
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+  template<>
+    struct __is_void<void>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+
+
+  template<typename _Tp>
+    struct __is_integer
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+
+
+
+
+  template<>
+    struct __is_integer<bool>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<signed char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<unsigned char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  template<>
+    struct __is_integer<wchar_t>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+# 184 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+  template<>
+    struct __is_integer<char16_t>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<char32_t>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  template<>
+    struct __is_integer<short>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<unsigned short>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<int>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<unsigned int>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<long>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<unsigned long>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<long long>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_integer<unsigned long long>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+# 272 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+__extension__ template<> struct __is_integer<__int128> { enum { __value = 1 }; typedef __true_type __type; }; __extension__ template<> struct __is_integer<unsigned __int128> { enum { __value = 1 }; typedef __true_type __type; };
+# 289 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+  template<typename _Tp>
+    struct __is_floating
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+
+  template<>
+    struct __is_floating<float>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_floating<double>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_floating<long double>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+# 366 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+  template<typename _Tp>
+    struct __is_pointer
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+  template<typename _Tp>
+    struct __is_pointer<_Tp*>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+
+
+  template<typename _Tp>
+    struct __is_arithmetic
+    : public __traitor<__is_integer<_Tp>, __is_floating<_Tp> >
+    { };
+
+
+
+
+  template<typename _Tp>
+    struct __is_scalar
+    : public __traitor<__is_arithmetic<_Tp>, __is_pointer<_Tp> >
+    { };
+
+
+
+
+  template<typename _Tp>
+    struct __is_char
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+  template<>
+    struct __is_char<char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  template<>
+    struct __is_char<wchar_t>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  template<typename _Tp>
+    struct __is_byte
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+  template<>
+    struct __is_byte<char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_byte<signed char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<>
+    struct __is_byte<unsigned char>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+
+  enum class byte : unsigned char;
+
+  template<>
+    struct __is_byte<byte>
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+# 470 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+  template<typename> struct iterator_traits;
+
+
+  template<typename _Tp>
+    struct __is_nonvolatile_trivially_copyable
+    {
+      enum { __value = __is_trivially_copyable(_Tp) };
+    };
+
+
+
+
+  template<typename _Tp>
+    struct __is_nonvolatile_trivially_copyable<volatile _Tp>
+    {
+      enum { __value = 0 };
+    };
+
+
+  template<typename _OutputIter, typename _InputIter>
+    struct __memcpyable
+    {
+      enum { __value = 0 };
+    };
+
+  template<typename _Tp>
+    struct __memcpyable<_Tp*, _Tp*>
+    : __is_nonvolatile_trivially_copyable<_Tp>
+    { };
+
+  template<typename _Tp>
+    struct __memcpyable<_Tp*, const _Tp*>
+    : __is_nonvolatile_trivially_copyable<_Tp>
+    { };
+
+
+
+
+
+
+  template<typename _Iter1, typename _Iter2>
+    struct __memcmpable
+    {
+      enum { __value = 0 };
+    };
+
+
+  template<typename _Tp>
+    struct __memcmpable<_Tp*, _Tp*>
+    : __is_nonvolatile_trivially_copyable<_Tp>
+    { };
+
+  template<typename _Tp>
+    struct __memcmpable<const _Tp*, _Tp*>
+    : __is_nonvolatile_trivially_copyable<_Tp>
+    { };
+
+  template<typename _Tp>
+    struct __memcmpable<_Tp*, const _Tp*>
+    : __is_nonvolatile_trivially_copyable<_Tp>
+    { };
+
+
+
+
+
+
+
+  template<typename _Tp, bool _TreatAsBytes =
+
+
+
+ __is_byte<_Tp>::__value
+
+    >
+    struct __is_memcmp_ordered
+    {
+      static const bool __value = _Tp(-1) > _Tp(1);
+    };
+
+  template<typename _Tp>
+    struct __is_memcmp_ordered<_Tp, false>
+    {
+      static const bool __value = false;
+    };
+
+
+  template<typename _Tp, typename _Up, bool = sizeof(_Tp) == sizeof(_Up)>
+    struct __is_memcmp_ordered_with
+    {
+      static const bool __value = __is_memcmp_ordered<_Tp>::__value
+ && __is_memcmp_ordered<_Up>::__value;
+    };
+
+  template<typename _Tp, typename _Up>
+    struct __is_memcmp_ordered_with<_Tp, _Up, false>
+    {
+      static const bool __value = false;
+    };
+# 579 "/usr/include/c++/13/bits/cpp_type_traits.h" 3
+  template<>
+    struct __is_memcmp_ordered_with<std::byte, std::byte, true>
+    { static constexpr bool __value = true; };
+
+  template<typename _Tp, bool _SameSize>
+    struct __is_memcmp_ordered_with<_Tp, std::byte, _SameSize>
+    { static constexpr bool __value = false; };
+
+  template<typename _Up, bool _SameSize>
+    struct __is_memcmp_ordered_with<std::byte, _Up, _SameSize>
+    { static constexpr bool __value = false; };
+
+
+
+
+
+  template<typename _Tp>
+    struct __is_move_iterator
+    {
+      enum { __value = 0 };
+      typedef __false_type __type;
+    };
+
+
+
+  template<typename _Iterator>
+   
+    inline _Iterator
+    __miter_base(_Iterator __it)
+    { return __it; }
+
+
+}
+}
+# 45 "/usr/include/c++/13/cmath" 2 3
+# 1 "/usr/include/c++/13/ext/type_traits.h" 1 3
+# 32 "/usr/include/c++/13/ext/type_traits.h" 3
+       
+# 33 "/usr/include/c++/13/ext/type_traits.h" 3
+
+
+
+
+extern "C++" {
+
+namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+  template<bool, typename>
+    struct __enable_if
+    { };
+
+  template<typename _Tp>
+    struct __enable_if<true, _Tp>
+    { typedef _Tp __type; };
+
+
+
+  template<bool _Cond, typename _Iftrue, typename _Iffalse>
+    struct __conditional_type
+    { typedef _Iftrue __type; };
+
+  template<typename _Iftrue, typename _Iffalse>
+    struct __conditional_type<false, _Iftrue, _Iffalse>
+    { typedef _Iffalse __type; };
+
+
+
+  template<typename _Tp>
+    struct __add_unsigned
+    {
+    private:
+      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;
+
+    public:
+      typedef typename __if_type::__type __type;
+    };
+
+  template<>
+    struct __add_unsigned<char>
+    { typedef unsigned char __type; };
+
+  template<>
+    struct __add_unsigned<signed char>
+    { typedef unsigned char __type; };
+
+  template<>
+    struct __add_unsigned<short>
+    { typedef unsigned short __type; };
+
+  template<>
+    struct __add_unsigned<int>
+    { typedef unsigned int __type; };
+
+  template<>
+    struct __add_unsigned<long>
+    { typedef unsigned long __type; };
+
+  template<>
+    struct __add_unsigned<long long>
+    { typedef unsigned long long __type; };
+
+
+  template<>
+    struct __add_unsigned<bool>;
+
+  template<>
+    struct __add_unsigned<wchar_t>;
+
+
+
+  template<typename _Tp>
+    struct __remove_unsigned
+    {
+    private:
+      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;
+
+    public:
+      typedef typename __if_type::__type __type;
+    };
+
+  template<>
+    struct __remove_unsigned<char>
+    { typedef signed char __type; };
+
+  template<>
+    struct __remove_unsigned<unsigned char>
+    { typedef signed char __type; };
+
+  template<>
+    struct __remove_unsigned<unsigned short>
+    { typedef short __type; };
+
+  template<>
+    struct __remove_unsigned<unsigned int>
+    { typedef int __type; };
+
+  template<>
+    struct __remove_unsigned<unsigned long>
+    { typedef long __type; };
+
+  template<>
+    struct __remove_unsigned<unsigned long long>
+    { typedef long long __type; };
+
+
+  template<>
+    struct __remove_unsigned<bool>;
+
+  template<>
+    struct __remove_unsigned<wchar_t>;
+
+
+
+  template<typename _Type>
+    constexpr
+    inline bool
+    __is_null_pointer(_Type* __ptr)
+    { return __ptr == 0; }
+
+  template<typename _Type>
+    constexpr
+    inline bool
+    __is_null_pointer(_Type)
+    { return false; }
+
+
+  constexpr bool
+  __is_null_pointer(std::nullptr_t)
+  { return true; }
+
+
+
+
+  template<typename _Tp, bool = std::__is_integer<_Tp>::__value>
+    struct __promote
+    { typedef double __type; };
+
+
+
+
+  template<typename _Tp>
+    struct __promote<_Tp, false>
+    { };
+
+  template<>
+    struct __promote<long double>
+    { typedef long double __type; };
+
+  template<>
+    struct __promote<double>
+    { typedef double __type; };
+
+  template<>
+    struct __promote<float>
+    { typedef float __type; };
+# 225 "/usr/include/c++/13/ext/type_traits.h" 3
+  template<typename... _Tp>
+    using __promoted_t = decltype((typename __promote<_Tp>::__type(0) + ...));
+
+
+
+  template<typename _Tp, typename _Up>
+    using __promote_2 = __promote<__promoted_t<_Tp, _Up>>;
+
+  template<typename _Tp, typename _Up, typename _Vp>
+    using __promote_3 = __promote<__promoted_t<_Tp, _Up, _Vp>>;
+
+  template<typename _Tp, typename _Up, typename _Vp, typename _Wp>
+    using __promote_4 = __promote<__promoted_t<_Tp, _Up, _Vp, _Wp>>;
+# 269 "/usr/include/c++/13/ext/type_traits.h" 3
+
+}
+}
+# 46 "/usr/include/c++/13/cmath" 2 3
+
+# 1 "/usr/include/math.h" 1 3 4
+# 27 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
+# 28 "/usr/include/math.h" 2 3 4
+
+
+
+
+
+
+extern "C" {
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/bits/types.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 28 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/timesize.h" 1 3 4
+# 29 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
+
+
+typedef unsigned char __u_char;
+typedef unsigned short int __u_short;
+typedef unsigned int __u_int;
+typedef unsigned long int __u_long;
+
+
+typedef signed char __int8_t;
+typedef unsigned char __uint8_t;
+typedef signed short int __int16_t;
+typedef unsigned short int __uint16_t;
+typedef signed int __int32_t;
+typedef unsigned int __uint32_t;
+
+typedef signed long int __int64_t;
+typedef unsigned long int __uint64_t;
+
+
+
+
+
+
+typedef __int8_t __int_least8_t;
+typedef __uint8_t __uint_least8_t;
+typedef __int16_t __int_least16_t;
+typedef __uint16_t __uint_least16_t;
+typedef __int32_t __int_least32_t;
+typedef __uint32_t __uint_least32_t;
+typedef __int64_t __int_least64_t;
+typedef __uint64_t __uint_least64_t;
+
+
+
+typedef long int __quad_t;
+typedef unsigned long int __u_quad_t;
+
+
+
+
+
+
+
+typedef long int __intmax_t;
+typedef unsigned long int __uintmax_t;
+# 141 "/usr/include/aarch64-linux-gnu/bits/types.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/typesizes.h" 1 3 4
+# 142 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/time64.h" 1 3 4
+# 143 "/usr/include/aarch64-linux-gnu/bits/types.h" 2 3 4
+
+
+typedef unsigned long int __dev_t;
+typedef unsigned int __uid_t;
+typedef unsigned int __gid_t;
+typedef unsigned long int __ino_t;
+typedef unsigned long int __ino64_t;
+typedef unsigned int __mode_t;
+typedef unsigned int __nlink_t;
+typedef long int __off_t;
+typedef long int __off64_t;
+typedef int __pid_t;
+typedef struct { int __val[2]; } __fsid_t;
+typedef long int __clock_t;
+typedef unsigned long int __rlim_t;
+typedef unsigned long int __rlim64_t;
+typedef unsigned int __id_t;
+typedef long int __time_t;
+typedef unsigned int __useconds_t;
+typedef long int __suseconds_t;
+typedef long int __suseconds64_t;
+
+typedef int __daddr_t;
+typedef int __key_t;
+
+
+typedef int __clockid_t;
+
+
+typedef void * __timer_t;
+
+
+typedef int __blksize_t;
+
+
+
+
+typedef long int __blkcnt_t;
+typedef long int __blkcnt64_t;
+
+
+typedef unsigned long int __fsblkcnt_t;
+typedef unsigned long int __fsblkcnt64_t;
+
+
+typedef unsigned long int __fsfilcnt_t;
+typedef unsigned long int __fsfilcnt64_t;
+
+
+typedef long int __fsword_t;
+
+typedef long int __ssize_t;
+
+
+typedef long int __syscall_slong_t;
+
+typedef unsigned long int __syscall_ulong_t;
+
+
+
+typedef __off64_t __loff_t;
+typedef char *__caddr_t;
+
+
+typedef long int __intptr_t;
+
+
+typedef unsigned int __socklen_t;
+
+
+
+
+typedef int __sig_atomic_t;
+# 38 "/usr/include/math.h" 2 3 4
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 1 3 4
+# 26 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libm-simd-decl-stubs.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 2 3 4
+# 96 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 3 4
+typedef __Float32x4_t __f32x4_t;
+typedef __Float64x2_t __f64x2_t;
+# 106 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 3 4
+typedef __SVFloat32_t __sv_f32_t;
+typedef __SVFloat64_t __sv_f64_t;
+typedef __SVBool_t __sv_bool_t;
+# 118 "/usr/include/aarch64-linux-gnu/bits/math-vector.h" 3 4
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_asinf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_atanf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_expf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_exp10f (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_exp2f (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_expm1f (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_logf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_log10f (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_log1pf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_log2f (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_sinf (__f32x4_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f32x4_t _ZGVnN4v_tanf (__f32x4_t);
+
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_acos (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_asin (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_atan (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_cos (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_exp (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_exp10 (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_exp2 (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_expm1 (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_log (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_log10 (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_log1p (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_log2 (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_sin (__f64x2_t);
+__attribute__ ((__aarch64_vector_pcs__)) __f64x2_t _ZGVnN2v_tan (__f64x2_t);
+
+
+
+
+
+
+__sv_f32_t _ZGVsMxvv_atan2f (__sv_f32_t, __sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_exp2f (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_expm1f (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_logf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_log10f (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_log1pf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t);
+
+__sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_exp2 (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_expm1 (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_log (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_log10 (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_log1p (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_log2 (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_sin (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_tan (__sv_f64_t, __sv_bool_t);
+# 41 "/usr/include/math.h" 2 3 4
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 1 3 4
+# 23 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 2 3 4
+# 95 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/long-double.h" 1 3 4
+# 25 "/usr/include/aarch64-linux-gnu/bits/floatn-common.h" 2 3 4
+# 96 "/usr/include/aarch64-linux-gnu/bits/floatn.h" 2 3 4
+# 44 "/usr/include/math.h" 2 3 4
+# 152 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/flt-eval-method.h" 1 3 4
+# 153 "/usr/include/math.h" 2 3 4
+# 163 "/usr/include/math.h" 3 4
+typedef float float_t;
+typedef double double_t;
+# 204 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/fp-logb.h" 1 3 4
+# 205 "/usr/include/math.h" 2 3 4
+# 247 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/fp-fast.h" 1 3 4
+# 248 "/usr/include/math.h" 2 3 4
+
+
+
+enum
+  {
+    FP_INT_UPWARD =
+
+      0,
+    FP_INT_DOWNWARD =
+
+      1,
+    FP_INT_TOWARDZERO =
+
+      2,
+    FP_INT_TONEARESTFROMZERO =
+
+      3,
+    FP_INT_TONEAREST =
+
+      4,
+  };
+# 312 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
+# 20 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
+extern int __fpclassify (double __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+extern int __signbit (double __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+
+extern int __isinf (double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __finite (double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __isnan (double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __iseqsig (double __x, double __y) noexcept (true);
+
+
+extern int __issignaling (double __value) noexcept (true)
+     __attribute__ ((__const__));
+# 313 "/usr/include/math.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern double acos (double __x) noexcept (true); extern double __acos (double __x) noexcept (true);
+
+ extern double asin (double __x) noexcept (true); extern double __asin (double __x) noexcept (true);
+
+ extern double atan (double __x) noexcept (true); extern double __atan (double __x) noexcept (true);
+
+ extern double atan2 (double __y, double __x) noexcept (true); extern double __atan2 (double __y, double __x) noexcept (true);
+
+
+ extern double cos (double __x) noexcept (true); extern double __cos (double __x) noexcept (true);
+
+ extern double sin (double __x) noexcept (true); extern double __sin (double __x) noexcept (true);
+
+ extern double tan (double __x) noexcept (true); extern double __tan (double __x) noexcept (true);
+
+
+
+
+ extern double cosh (double __x) noexcept (true); extern double __cosh (double __x) noexcept (true);
+
+ extern double sinh (double __x) noexcept (true); extern double __sinh (double __x) noexcept (true);
+
+ extern double tanh (double __x) noexcept (true); extern double __tanh (double __x) noexcept (true);
+
+
+
+ extern void sincos (double __x, double *__sinx, double *__cosx) noexcept (true); extern void __sincos (double __x, double *__sinx, double *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern double acosh (double __x) noexcept (true); extern double __acosh (double __x) noexcept (true);
+
+ extern double asinh (double __x) noexcept (true); extern double __asinh (double __x) noexcept (true);
+
+ extern double atanh (double __x) noexcept (true); extern double __atanh (double __x) noexcept (true);
+
+
+
+
+
+ extern double exp (double __x) noexcept (true); extern double __exp (double __x) noexcept (true);
+
+
+extern double frexp (double __x, int *__exponent) noexcept (true); extern double __frexp (double __x, int *__exponent) noexcept (true);
+
+
+extern double ldexp (double __x, int __exponent) noexcept (true); extern double __ldexp (double __x, int __exponent) noexcept (true);
+
+
+ extern double log (double __x) noexcept (true); extern double __log (double __x) noexcept (true);
+
+
+ extern double log10 (double __x) noexcept (true); extern double __log10 (double __x) noexcept (true);
+
+
+extern double modf (double __x, double *__iptr) noexcept (true); extern double __modf (double __x, double *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern double exp10 (double __x) noexcept (true); extern double __exp10 (double __x) noexcept (true);
+
+
+
+
+ extern double expm1 (double __x) noexcept (true); extern double __expm1 (double __x) noexcept (true);
+
+
+ extern double log1p (double __x) noexcept (true); extern double __log1p (double __x) noexcept (true);
+
+
+extern double logb (double __x) noexcept (true); extern double __logb (double __x) noexcept (true);
+
+
+
+
+ extern double exp2 (double __x) noexcept (true); extern double __exp2 (double __x) noexcept (true);
+
+
+ extern double log2 (double __x) noexcept (true); extern double __log2 (double __x) noexcept (true);
+
+
+
+
+
+
+ extern double pow (double __x, double __y) noexcept (true); extern double __pow (double __x, double __y) noexcept (true);
+
+
+extern double sqrt (double __x) noexcept (true); extern double __sqrt (double __x) noexcept (true);
+
+
+
+ extern double hypot (double __x, double __y) noexcept (true); extern double __hypot (double __x, double __y) noexcept (true);
+
+
+
+
+ extern double cbrt (double __x) noexcept (true); extern double __cbrt (double __x) noexcept (true);
+
+
+
+
+
+
+extern double ceil (double __x) noexcept (true) __attribute__ ((__const__)); extern double __ceil (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fabs (double __x) noexcept (true) __attribute__ ((__const__)); extern double __fabs (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern double floor (double __x) noexcept (true) __attribute__ ((__const__)); extern double __floor (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fmod (double __x, double __y) noexcept (true); extern double __fmod (double __x, double __y) noexcept (true);
+# 183 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern int finite (double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern double drem (double __x, double __y) noexcept (true); extern double __drem (double __x, double __y) noexcept (true);
+
+
+
+extern double significand (double __x) noexcept (true); extern double __significand (double __x) noexcept (true);
+
+
+
+
+
+
+extern double copysign (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __copysign (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern double nan (const char *__tagb) noexcept (true); extern double __nan (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern double j0 (double) noexcept (true); extern double __j0 (double) noexcept (true);
+extern double j1 (double) noexcept (true); extern double __j1 (double) noexcept (true);
+extern double jn (int, double) noexcept (true); extern double __jn (int, double) noexcept (true);
+extern double y0 (double) noexcept (true); extern double __y0 (double) noexcept (true);
+extern double y1 (double) noexcept (true); extern double __y1 (double) noexcept (true);
+extern double yn (int, double) noexcept (true); extern double __yn (int, double) noexcept (true);
+
+
+
+
+
+ extern double erf (double) noexcept (true); extern double __erf (double) noexcept (true);
+ extern double erfc (double) noexcept (true); extern double __erfc (double) noexcept (true);
+extern double lgamma (double) noexcept (true); extern double __lgamma (double) noexcept (true);
+
+
+
+
+extern double tgamma (double) noexcept (true); extern double __tgamma (double) noexcept (true);
+
+
+
+
+
+extern double gamma (double) noexcept (true); extern double __gamma (double) noexcept (true);
+
+
+
+
+
+
+
+extern double lgamma_r (double, int *__signgamp) noexcept (true); extern double __lgamma_r (double, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern double rint (double __x) noexcept (true); extern double __rint (double __x) noexcept (true);
+
+
+extern double nextafter (double __x, double __y) noexcept (true); extern double __nextafter (double __x, double __y) noexcept (true);
+
+extern double nexttoward (double __x, long double __y) noexcept (true); extern double __nexttoward (double __x, long double __y) noexcept (true);
+
+
+
+
+extern double nextdown (double __x) noexcept (true); extern double __nextdown (double __x) noexcept (true);
+
+extern double nextup (double __x) noexcept (true); extern double __nextup (double __x) noexcept (true);
+
+
+
+extern double remainder (double __x, double __y) noexcept (true); extern double __remainder (double __x, double __y) noexcept (true);
+
+
+
+extern double scalbn (double __x, int __n) noexcept (true); extern double __scalbn (double __x, int __n) noexcept (true);
+
+
+
+extern int ilogb (double __x) noexcept (true); extern int __ilogb (double __x) noexcept (true);
+
+
+
+
+extern long int llogb (double __x) noexcept (true); extern long int __llogb (double __x) noexcept (true);
+
+
+
+
+extern double scalbln (double __x, long int __n) noexcept (true); extern double __scalbln (double __x, long int __n) noexcept (true);
+
+
+
+extern double nearbyint (double __x) noexcept (true); extern double __nearbyint (double __x) noexcept (true);
+
+
+
+extern double round (double __x) noexcept (true) __attribute__ ((__const__)); extern double __round (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern double trunc (double __x) noexcept (true) __attribute__ ((__const__)); extern double __trunc (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern double remquo (double __x, double __y, int *__quo) noexcept (true); extern double __remquo (double __x, double __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrint (double __x) noexcept (true); extern long int __lrint (double __x) noexcept (true);
+__extension__
+extern long long int llrint (double __x) noexcept (true); extern long long int __llrint (double __x) noexcept (true);
+
+
+
+extern long int lround (double __x) noexcept (true); extern long int __lround (double __x) noexcept (true);
+__extension__
+extern long long int llround (double __x) noexcept (true); extern long long int __llround (double __x) noexcept (true);
+
+
+
+extern double fdim (double __x, double __y) noexcept (true); extern double __fdim (double __x, double __y) noexcept (true);
+
+
+
+extern double fmax (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fmin (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern double fma (double __x, double __y, double __z) noexcept (true); extern double __fma (double __x, double __y, double __z) noexcept (true);
+
+
+
+
+extern double roundeven (double __x) noexcept (true) __attribute__ ((__const__)); extern double __roundeven (double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfp (double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfp (double __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfp (double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfp (double __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpx (double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpx (double __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpx (double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpx (double __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalize (double *__cx, const double *__x) noexcept (true);
+
+
+
+
+
+
+extern double fmaxmag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaxmag (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fminmag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminmag (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern double fmaximum (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fminimum (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fmaximum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fminimum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fmaximum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fminimum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fmaximum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern double fminimum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorder (const double *__x, const double *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermag (const double *__x, const double *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern double getpayload (const double *__x) noexcept (true); extern double __getpayload (const double *__x) noexcept (true);
+
+
+extern int setpayload (double *__x, double __payload) noexcept (true);
+
+
+extern int setpayloadsig (double *__x, double __payload) noexcept (true);
+
+
+
+
+
+
+
+extern double scalb (double __x, double __n) noexcept (true); extern double __scalb (double __x, double __n) noexcept (true);
+# 314 "/usr/include/math.h" 2 3 4
+# 329 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
+# 20 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
+extern int __fpclassifyf (float __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+extern int __signbitf (float __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+
+extern int __isinff (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __finitef (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __isnanf (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __iseqsigf (float __x, float __y) noexcept (true);
+
+
+extern int __issignalingf (float __value) noexcept (true)
+     __attribute__ ((__const__));
+# 330 "/usr/include/math.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern float acosf (float __x) noexcept (true); extern float __acosf (float __x) noexcept (true);
+
+ extern float asinf (float __x) noexcept (true); extern float __asinf (float __x) noexcept (true);
+
+ extern float atanf (float __x) noexcept (true); extern float __atanf (float __x) noexcept (true);
+
+ extern float atan2f (float __y, float __x) noexcept (true); extern float __atan2f (float __y, float __x) noexcept (true);
+
+
+ extern float cosf (float __x) noexcept (true); extern float __cosf (float __x) noexcept (true);
+
+ extern float sinf (float __x) noexcept (true); extern float __sinf (float __x) noexcept (true);
+
+ extern float tanf (float __x) noexcept (true); extern float __tanf (float __x) noexcept (true);
+
+
+
+
+ extern float coshf (float __x) noexcept (true); extern float __coshf (float __x) noexcept (true);
+
+ extern float sinhf (float __x) noexcept (true); extern float __sinhf (float __x) noexcept (true);
+
+ extern float tanhf (float __x) noexcept (true); extern float __tanhf (float __x) noexcept (true);
+
+
+
+ extern void sincosf (float __x, float *__sinx, float *__cosx) noexcept (true); extern void __sincosf (float __x, float *__sinx, float *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern float acoshf (float __x) noexcept (true); extern float __acoshf (float __x) noexcept (true);
+
+ extern float asinhf (float __x) noexcept (true); extern float __asinhf (float __x) noexcept (true);
+
+ extern float atanhf (float __x) noexcept (true); extern float __atanhf (float __x) noexcept (true);
+
+
+
+
+
+ extern float expf (float __x) noexcept (true); extern float __expf (float __x) noexcept (true);
+
+
+extern float frexpf (float __x, int *__exponent) noexcept (true); extern float __frexpf (float __x, int *__exponent) noexcept (true);
+
+
+extern float ldexpf (float __x, int __exponent) noexcept (true); extern float __ldexpf (float __x, int __exponent) noexcept (true);
+
+
+ extern float logf (float __x) noexcept (true); extern float __logf (float __x) noexcept (true);
+
+
+ extern float log10f (float __x) noexcept (true); extern float __log10f (float __x) noexcept (true);
+
+
+extern float modff (float __x, float *__iptr) noexcept (true); extern float __modff (float __x, float *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern float exp10f (float __x) noexcept (true); extern float __exp10f (float __x) noexcept (true);
+
+
+
+
+ extern float expm1f (float __x) noexcept (true); extern float __expm1f (float __x) noexcept (true);
+
+
+ extern float log1pf (float __x) noexcept (true); extern float __log1pf (float __x) noexcept (true);
+
+
+extern float logbf (float __x) noexcept (true); extern float __logbf (float __x) noexcept (true);
+
+
+
+
+ extern float exp2f (float __x) noexcept (true); extern float __exp2f (float __x) noexcept (true);
+
+
+ extern float log2f (float __x) noexcept (true); extern float __log2f (float __x) noexcept (true);
+
+
+
+
+
+
+ extern float powf (float __x, float __y) noexcept (true); extern float __powf (float __x, float __y) noexcept (true);
+
+
+extern float sqrtf (float __x) noexcept (true); extern float __sqrtf (float __x) noexcept (true);
+
+
+
+ extern float hypotf (float __x, float __y) noexcept (true); extern float __hypotf (float __x, float __y) noexcept (true);
+
+
+
+
+ extern float cbrtf (float __x) noexcept (true); extern float __cbrtf (float __x) noexcept (true);
+
+
+
+
+
+
+extern float ceilf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __ceilf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fabsf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __fabsf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern float floorf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __floorf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fmodf (float __x, float __y) noexcept (true); extern float __fmodf (float __x, float __y) noexcept (true);
+# 177 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern int isinff (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+
+
+extern int finitef (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern float dremf (float __x, float __y) noexcept (true); extern float __dremf (float __x, float __y) noexcept (true);
+
+
+
+extern float significandf (float __x) noexcept (true); extern float __significandf (float __x) noexcept (true);
+
+
+
+
+
+
+extern float copysignf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __copysignf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern float nanf (const char *__tagb) noexcept (true); extern float __nanf (const char *__tagb) noexcept (true);
+# 213 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern int isnanf (float __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+
+
+
+extern float j0f (float) noexcept (true); extern float __j0f (float) noexcept (true);
+extern float j1f (float) noexcept (true); extern float __j1f (float) noexcept (true);
+extern float jnf (int, float) noexcept (true); extern float __jnf (int, float) noexcept (true);
+extern float y0f (float) noexcept (true); extern float __y0f (float) noexcept (true);
+extern float y1f (float) noexcept (true); extern float __y1f (float) noexcept (true);
+extern float ynf (int, float) noexcept (true); extern float __ynf (int, float) noexcept (true);
+
+
+
+
+
+ extern float erff (float) noexcept (true); extern float __erff (float) noexcept (true);
+ extern float erfcf (float) noexcept (true); extern float __erfcf (float) noexcept (true);
+extern float lgammaf (float) noexcept (true); extern float __lgammaf (float) noexcept (true);
+
+
+
+
+extern float tgammaf (float) noexcept (true); extern float __tgammaf (float) noexcept (true);
+
+
+
+
+
+extern float gammaf (float) noexcept (true); extern float __gammaf (float) noexcept (true);
+
+
+
+
+
+
+
+extern float lgammaf_r (float, int *__signgamp) noexcept (true); extern float __lgammaf_r (float, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern float rintf (float __x) noexcept (true); extern float __rintf (float __x) noexcept (true);
+
+
+extern float nextafterf (float __x, float __y) noexcept (true); extern float __nextafterf (float __x, float __y) noexcept (true);
+
+extern float nexttowardf (float __x, long double __y) noexcept (true); extern float __nexttowardf (float __x, long double __y) noexcept (true);
+
+
+
+
+extern float nextdownf (float __x) noexcept (true); extern float __nextdownf (float __x) noexcept (true);
+
+extern float nextupf (float __x) noexcept (true); extern float __nextupf (float __x) noexcept (true);
+
+
+
+extern float remainderf (float __x, float __y) noexcept (true); extern float __remainderf (float __x, float __y) noexcept (true);
+
+
+
+extern float scalbnf (float __x, int __n) noexcept (true); extern float __scalbnf (float __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf (float __x) noexcept (true); extern int __ilogbf (float __x) noexcept (true);
+
+
+
+
+extern long int llogbf (float __x) noexcept (true); extern long int __llogbf (float __x) noexcept (true);
+
+
+
+
+extern float scalblnf (float __x, long int __n) noexcept (true); extern float __scalblnf (float __x, long int __n) noexcept (true);
+
+
+
+extern float nearbyintf (float __x) noexcept (true); extern float __nearbyintf (float __x) noexcept (true);
+
+
+
+extern float roundf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __roundf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern float truncf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __truncf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern float remquof (float __x, float __y, int *__quo) noexcept (true); extern float __remquof (float __x, float __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf (float __x) noexcept (true); extern long int __lrintf (float __x) noexcept (true);
+__extension__
+extern long long int llrintf (float __x) noexcept (true); extern long long int __llrintf (float __x) noexcept (true);
+
+
+
+extern long int lroundf (float __x) noexcept (true); extern long int __lroundf (float __x) noexcept (true);
+__extension__
+extern long long int llroundf (float __x) noexcept (true); extern long long int __llroundf (float __x) noexcept (true);
+
+
+
+extern float fdimf (float __x, float __y) noexcept (true); extern float __fdimf (float __x, float __y) noexcept (true);
+
+
+
+extern float fmaxf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaxf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern float fmaf (float __x, float __y, float __z) noexcept (true); extern float __fmaf (float __x, float __y, float __z) noexcept (true);
+
+
+
+
+extern float roundevenf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __roundevenf (float __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf (float __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf (float __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf (float __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf (float __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf (float __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf (float __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf (float __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf (float __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef (float *__cx, const float *__x) noexcept (true);
+
+
+
+
+
+
+extern float fmaxmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaxmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern float fmaximumf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximumf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminimumf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimumf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fmaximum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminimum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fmaximum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminimum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fmaximum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern float fminimum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf (const float *__x, const float *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf (const float *__x, const float *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern float getpayloadf (const float *__x) noexcept (true); extern float __getpayloadf (const float *__x) noexcept (true);
+
+
+extern int setpayloadf (float *__x, float __payload) noexcept (true);
+
+
+extern int setpayloadsigf (float *__x, float __payload) noexcept (true);
+
+
+
+
+
+
+
+extern float scalbf (float __x, float __n) noexcept (true); extern float __scalbf (float __x, float __n) noexcept (true);
+# 331 "/usr/include/math.h" 2 3 4
+# 398 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
+# 20 "/usr/include/aarch64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
+extern int __fpclassifyl (long double __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+extern int __signbitl (long double __value) noexcept (true)
+     __attribute__ ((__const__));
+
+
+
+extern int __isinfl (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __finitel (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __isnanl (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern int __iseqsigl (long double __x, long double __y) noexcept (true);
+
+
+extern int __issignalingl (long double __value) noexcept (true)
+     __attribute__ ((__const__));
+# 399 "/usr/include/math.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern long double acosl (long double __x) noexcept (true); extern long double __acosl (long double __x) noexcept (true);
+
+ extern long double asinl (long double __x) noexcept (true); extern long double __asinl (long double __x) noexcept (true);
+
+ extern long double atanl (long double __x) noexcept (true); extern long double __atanl (long double __x) noexcept (true);
+
+ extern long double atan2l (long double __y, long double __x) noexcept (true); extern long double __atan2l (long double __y, long double __x) noexcept (true);
+
+
+ extern long double cosl (long double __x) noexcept (true); extern long double __cosl (long double __x) noexcept (true);
+
+ extern long double sinl (long double __x) noexcept (true); extern long double __sinl (long double __x) noexcept (true);
+
+ extern long double tanl (long double __x) noexcept (true); extern long double __tanl (long double __x) noexcept (true);
+
+
+
+
+ extern long double coshl (long double __x) noexcept (true); extern long double __coshl (long double __x) noexcept (true);
+
+ extern long double sinhl (long double __x) noexcept (true); extern long double __sinhl (long double __x) noexcept (true);
+
+ extern long double tanhl (long double __x) noexcept (true); extern long double __tanhl (long double __x) noexcept (true);
+
+
+
+ extern void sincosl (long double __x, long double *__sinx, long double *__cosx) noexcept (true); extern void __sincosl (long double __x, long double *__sinx, long double *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern long double acoshl (long double __x) noexcept (true); extern long double __acoshl (long double __x) noexcept (true);
+
+ extern long double asinhl (long double __x) noexcept (true); extern long double __asinhl (long double __x) noexcept (true);
+
+ extern long double atanhl (long double __x) noexcept (true); extern long double __atanhl (long double __x) noexcept (true);
+
+
+
+
+
+ extern long double expl (long double __x) noexcept (true); extern long double __expl (long double __x) noexcept (true);
+
+
+extern long double frexpl (long double __x, int *__exponent) noexcept (true); extern long double __frexpl (long double __x, int *__exponent) noexcept (true);
+
+
+extern long double ldexpl (long double __x, int __exponent) noexcept (true); extern long double __ldexpl (long double __x, int __exponent) noexcept (true);
+
+
+ extern long double logl (long double __x) noexcept (true); extern long double __logl (long double __x) noexcept (true);
+
+
+ extern long double log10l (long double __x) noexcept (true); extern long double __log10l (long double __x) noexcept (true);
+
+
+extern long double modfl (long double __x, long double *__iptr) noexcept (true); extern long double __modfl (long double __x, long double *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern long double exp10l (long double __x) noexcept (true); extern long double __exp10l (long double __x) noexcept (true);
+
+
+
+
+ extern long double expm1l (long double __x) noexcept (true); extern long double __expm1l (long double __x) noexcept (true);
+
+
+ extern long double log1pl (long double __x) noexcept (true); extern long double __log1pl (long double __x) noexcept (true);
+
+
+extern long double logbl (long double __x) noexcept (true); extern long double __logbl (long double __x) noexcept (true);
+
+
+
+
+ extern long double exp2l (long double __x) noexcept (true); extern long double __exp2l (long double __x) noexcept (true);
+
+
+ extern long double log2l (long double __x) noexcept (true); extern long double __log2l (long double __x) noexcept (true);
+
+
+
+
+
+
+ extern long double powl (long double __x, long double __y) noexcept (true); extern long double __powl (long double __x, long double __y) noexcept (true);
+
+
+extern long double sqrtl (long double __x) noexcept (true); extern long double __sqrtl (long double __x) noexcept (true);
+
+
+
+ extern long double hypotl (long double __x, long double __y) noexcept (true); extern long double __hypotl (long double __x, long double __y) noexcept (true);
+
+
+
+
+ extern long double cbrtl (long double __x) noexcept (true); extern long double __cbrtl (long double __x) noexcept (true);
+
+
+
+
+
+
+extern long double ceill (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __ceill (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fabsl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __fabsl (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double floorl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __floorl (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fmodl (long double __x, long double __y) noexcept (true); extern long double __fmodl (long double __x, long double __y) noexcept (true);
+# 177 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern int isinfl (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+
+
+extern int finitel (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+extern long double dreml (long double __x, long double __y) noexcept (true); extern long double __dreml (long double __x, long double __y) noexcept (true);
+
+
+
+extern long double significandl (long double __x) noexcept (true); extern long double __significandl (long double __x) noexcept (true);
+
+
+
+
+
+
+extern long double copysignl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __copysignl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern long double nanl (const char *__tagb) noexcept (true); extern long double __nanl (const char *__tagb) noexcept (true);
+# 213 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern int isnanl (long double __value) noexcept (true)
+  __attribute__ ((__const__));
+
+
+
+
+
+extern long double j0l (long double) noexcept (true); extern long double __j0l (long double) noexcept (true);
+extern long double j1l (long double) noexcept (true); extern long double __j1l (long double) noexcept (true);
+extern long double jnl (int, long double) noexcept (true); extern long double __jnl (int, long double) noexcept (true);
+extern long double y0l (long double) noexcept (true); extern long double __y0l (long double) noexcept (true);
+extern long double y1l (long double) noexcept (true); extern long double __y1l (long double) noexcept (true);
+extern long double ynl (int, long double) noexcept (true); extern long double __ynl (int, long double) noexcept (true);
+
+
+
+
+
+ extern long double erfl (long double) noexcept (true); extern long double __erfl (long double) noexcept (true);
+ extern long double erfcl (long double) noexcept (true); extern long double __erfcl (long double) noexcept (true);
+extern long double lgammal (long double) noexcept (true); extern long double __lgammal (long double) noexcept (true);
+
+
+
+
+extern long double tgammal (long double) noexcept (true); extern long double __tgammal (long double) noexcept (true);
+
+
+
+
+
+extern long double gammal (long double) noexcept (true); extern long double __gammal (long double) noexcept (true);
+
+
+
+
+
+
+
+extern long double lgammal_r (long double, int *__signgamp) noexcept (true); extern long double __lgammal_r (long double, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern long double rintl (long double __x) noexcept (true); extern long double __rintl (long double __x) noexcept (true);
+
+
+extern long double nextafterl (long double __x, long double __y) noexcept (true); extern long double __nextafterl (long double __x, long double __y) noexcept (true);
+
+extern long double nexttowardl (long double __x, long double __y) noexcept (true); extern long double __nexttowardl (long double __x, long double __y) noexcept (true);
+
+
+
+
+extern long double nextdownl (long double __x) noexcept (true); extern long double __nextdownl (long double __x) noexcept (true);
+
+extern long double nextupl (long double __x) noexcept (true); extern long double __nextupl (long double __x) noexcept (true);
+
+
+
+extern long double remainderl (long double __x, long double __y) noexcept (true); extern long double __remainderl (long double __x, long double __y) noexcept (true);
+
+
+
+extern long double scalbnl (long double __x, int __n) noexcept (true); extern long double __scalbnl (long double __x, int __n) noexcept (true);
+
+
+
+extern int ilogbl (long double __x) noexcept (true); extern int __ilogbl (long double __x) noexcept (true);
+
+
+
+
+extern long int llogbl (long double __x) noexcept (true); extern long int __llogbl (long double __x) noexcept (true);
+
+
+
+
+extern long double scalblnl (long double __x, long int __n) noexcept (true); extern long double __scalblnl (long double __x, long int __n) noexcept (true);
+
+
+
+extern long double nearbyintl (long double __x) noexcept (true); extern long double __nearbyintl (long double __x) noexcept (true);
+
+
+
+extern long double roundl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __roundl (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern long double truncl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __truncl (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern long double remquol (long double __x, long double __y, int *__quo) noexcept (true); extern long double __remquol (long double __x, long double __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintl (long double __x) noexcept (true); extern long int __lrintl (long double __x) noexcept (true);
+__extension__
+extern long long int llrintl (long double __x) noexcept (true); extern long long int __llrintl (long double __x) noexcept (true);
+
+
+
+extern long int lroundl (long double __x) noexcept (true); extern long int __lroundl (long double __x) noexcept (true);
+__extension__
+extern long long int llroundl (long double __x) noexcept (true); extern long long int __llroundl (long double __x) noexcept (true);
+
+
+
+extern long double fdiml (long double __x, long double __y) noexcept (true); extern long double __fdiml (long double __x, long double __y) noexcept (true);
+
+
+
+extern long double fmaxl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaxl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern long double fmal (long double __x, long double __y, long double __z) noexcept (true); extern long double __fmal (long double __x, long double __y, long double __z) noexcept (true);
+
+
+
+
+extern long double roundevenl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __roundevenl (long double __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpl (long double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpl (long double __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpl (long double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpl (long double __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxl (long double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxl (long double __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxl (long double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxl (long double __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizel (long double *__cx, const long double *__x) noexcept (true);
+
+
+
+
+
+
+extern long double fmaxmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaxmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern long double fmaximuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminimuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fmaximum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminimum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fmaximum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminimum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fmaximum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern long double fminimum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderl (const long double *__x, const long double *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagl (const long double *__x, const long double *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern long double getpayloadl (const long double *__x) noexcept (true); extern long double __getpayloadl (const long double *__x) noexcept (true);
+
+
+extern int setpayloadl (long double *__x, long double __payload) noexcept (true);
+
+
+extern int setpayloadsigl (long double *__x, long double __payload) noexcept (true);
+
+
+
+
+
+
+
+extern long double scalbl (long double __x, long double __n) noexcept (true); extern long double __scalbl (long double __x, long double __n) noexcept (true);
+# 400 "/usr/include/math.h" 2 3 4
+# 450 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern _Float32 acosf32 (_Float32 __x) noexcept (true); extern _Float32 __acosf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 asinf32 (_Float32 __x) noexcept (true); extern _Float32 __asinf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 atanf32 (_Float32 __x) noexcept (true); extern _Float32 __atanf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 atan2f32 (_Float32 __y, _Float32 __x) noexcept (true); extern _Float32 __atan2f32 (_Float32 __y, _Float32 __x) noexcept (true);
+
+
+ extern _Float32 cosf32 (_Float32 __x) noexcept (true); extern _Float32 __cosf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 sinf32 (_Float32 __x) noexcept (true); extern _Float32 __sinf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 tanf32 (_Float32 __x) noexcept (true); extern _Float32 __tanf32 (_Float32 __x) noexcept (true);
+
+
+
+
+ extern _Float32 coshf32 (_Float32 __x) noexcept (true); extern _Float32 __coshf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 sinhf32 (_Float32 __x) noexcept (true); extern _Float32 __sinhf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 tanhf32 (_Float32 __x) noexcept (true); extern _Float32 __tanhf32 (_Float32 __x) noexcept (true);
+
+
+
+ extern void sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) noexcept (true); extern void __sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern _Float32 acoshf32 (_Float32 __x) noexcept (true); extern _Float32 __acoshf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 asinhf32 (_Float32 __x) noexcept (true); extern _Float32 __asinhf32 (_Float32 __x) noexcept (true);
+
+ extern _Float32 atanhf32 (_Float32 __x) noexcept (true); extern _Float32 __atanhf32 (_Float32 __x) noexcept (true);
+
+
+
+
+
+ extern _Float32 expf32 (_Float32 __x) noexcept (true); extern _Float32 __expf32 (_Float32 __x) noexcept (true);
+
+
+extern _Float32 frexpf32 (_Float32 __x, int *__exponent) noexcept (true); extern _Float32 __frexpf32 (_Float32 __x, int *__exponent) noexcept (true);
+
+
+extern _Float32 ldexpf32 (_Float32 __x, int __exponent) noexcept (true); extern _Float32 __ldexpf32 (_Float32 __x, int __exponent) noexcept (true);
+
+
+ extern _Float32 logf32 (_Float32 __x) noexcept (true); extern _Float32 __logf32 (_Float32 __x) noexcept (true);
+
+
+ extern _Float32 log10f32 (_Float32 __x) noexcept (true); extern _Float32 __log10f32 (_Float32 __x) noexcept (true);
+
+
+extern _Float32 modff32 (_Float32 __x, _Float32 *__iptr) noexcept (true); extern _Float32 __modff32 (_Float32 __x, _Float32 *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern _Float32 exp10f32 (_Float32 __x) noexcept (true); extern _Float32 __exp10f32 (_Float32 __x) noexcept (true);
+
+
+
+
+ extern _Float32 expm1f32 (_Float32 __x) noexcept (true); extern _Float32 __expm1f32 (_Float32 __x) noexcept (true);
+
+
+ extern _Float32 log1pf32 (_Float32 __x) noexcept (true); extern _Float32 __log1pf32 (_Float32 __x) noexcept (true);
+
+
+extern _Float32 logbf32 (_Float32 __x) noexcept (true); extern _Float32 __logbf32 (_Float32 __x) noexcept (true);
+
+
+
+
+ extern _Float32 exp2f32 (_Float32 __x) noexcept (true); extern _Float32 __exp2f32 (_Float32 __x) noexcept (true);
+
+
+ extern _Float32 log2f32 (_Float32 __x) noexcept (true); extern _Float32 __log2f32 (_Float32 __x) noexcept (true);
+
+
+
+
+
+
+ extern _Float32 powf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __powf32 (_Float32 __x, _Float32 __y) noexcept (true);
+
+
+extern _Float32 sqrtf32 (_Float32 __x) noexcept (true); extern _Float32 __sqrtf32 (_Float32 __x) noexcept (true);
+
+
+
+ extern _Float32 hypotf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __hypotf32 (_Float32 __x, _Float32 __y) noexcept (true);
+
+
+
+
+ extern _Float32 cbrtf32 (_Float32 __x) noexcept (true); extern _Float32 __cbrtf32 (_Float32 __x) noexcept (true);
+
+
+
+
+
+
+extern _Float32 ceilf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __ceilf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fabsf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fabsf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 floorf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __floorf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fmodf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __fmodf32 (_Float32 __x, _Float32 __y) noexcept (true);
+# 198 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32 copysignf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __copysignf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32 nanf32 (const char *__tagb) noexcept (true); extern _Float32 __nanf32 (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32 j0f32 (_Float32) noexcept (true); extern _Float32 __j0f32 (_Float32) noexcept (true);
+extern _Float32 j1f32 (_Float32) noexcept (true); extern _Float32 __j1f32 (_Float32) noexcept (true);
+extern _Float32 jnf32 (int, _Float32) noexcept (true); extern _Float32 __jnf32 (int, _Float32) noexcept (true);
+extern _Float32 y0f32 (_Float32) noexcept (true); extern _Float32 __y0f32 (_Float32) noexcept (true);
+extern _Float32 y1f32 (_Float32) noexcept (true); extern _Float32 __y1f32 (_Float32) noexcept (true);
+extern _Float32 ynf32 (int, _Float32) noexcept (true); extern _Float32 __ynf32 (int, _Float32) noexcept (true);
+
+
+
+
+
+ extern _Float32 erff32 (_Float32) noexcept (true); extern _Float32 __erff32 (_Float32) noexcept (true);
+ extern _Float32 erfcf32 (_Float32) noexcept (true); extern _Float32 __erfcf32 (_Float32) noexcept (true);
+extern _Float32 lgammaf32 (_Float32) noexcept (true); extern _Float32 __lgammaf32 (_Float32) noexcept (true);
+
+
+
+
+extern _Float32 tgammaf32 (_Float32) noexcept (true); extern _Float32 __tgammaf32 (_Float32) noexcept (true);
+# 252 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32 lgammaf32_r (_Float32, int *__signgamp) noexcept (true); extern _Float32 __lgammaf32_r (_Float32, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern _Float32 rintf32 (_Float32 __x) noexcept (true); extern _Float32 __rintf32 (_Float32 __x) noexcept (true);
+
+
+extern _Float32 nextafterf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __nextafterf32 (_Float32 __x, _Float32 __y) noexcept (true);
+
+
+
+
+
+
+extern _Float32 nextdownf32 (_Float32 __x) noexcept (true); extern _Float32 __nextdownf32 (_Float32 __x) noexcept (true);
+
+extern _Float32 nextupf32 (_Float32 __x) noexcept (true); extern _Float32 __nextupf32 (_Float32 __x) noexcept (true);
+
+
+
+extern _Float32 remainderf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __remainderf32 (_Float32 __x, _Float32 __y) noexcept (true);
+
+
+
+extern _Float32 scalbnf32 (_Float32 __x, int __n) noexcept (true); extern _Float32 __scalbnf32 (_Float32 __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf32 (_Float32 __x) noexcept (true); extern int __ilogbf32 (_Float32 __x) noexcept (true);
+
+
+
+
+extern long int llogbf32 (_Float32 __x) noexcept (true); extern long int __llogbf32 (_Float32 __x) noexcept (true);
+
+
+
+
+extern _Float32 scalblnf32 (_Float32 __x, long int __n) noexcept (true); extern _Float32 __scalblnf32 (_Float32 __x, long int __n) noexcept (true);
+
+
+
+extern _Float32 nearbyintf32 (_Float32 __x) noexcept (true); extern _Float32 __nearbyintf32 (_Float32 __x) noexcept (true);
+
+
+
+extern _Float32 roundf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __roundf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float32 truncf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __truncf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32 remquof32 (_Float32 __x, _Float32 __y, int *__quo) noexcept (true); extern _Float32 __remquof32 (_Float32 __x, _Float32 __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf32 (_Float32 __x) noexcept (true); extern long int __lrintf32 (_Float32 __x) noexcept (true);
+__extension__
+extern long long int llrintf32 (_Float32 __x) noexcept (true); extern long long int __llrintf32 (_Float32 __x) noexcept (true);
+
+
+
+extern long int lroundf32 (_Float32 __x) noexcept (true); extern long int __lroundf32 (_Float32 __x) noexcept (true);
+__extension__
+extern long long int llroundf32 (_Float32 __x) noexcept (true); extern long long int __llroundf32 (_Float32 __x) noexcept (true);
+
+
+
+extern _Float32 fdimf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __fdimf32 (_Float32 __x, _Float32 __y) noexcept (true);
+
+
+
+extern _Float32 fmaxf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaxf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float32 fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) noexcept (true); extern _Float32 __fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) noexcept (true);
+
+
+
+
+extern _Float32 roundevenf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __roundevenf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef32 (_Float32 *__cx, const _Float32 *__x) noexcept (true);
+
+
+
+
+
+
+extern _Float32 fmaxmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaxmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32 fmaximumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminimumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fmaximum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminimum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fmaximum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminimum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fmaximum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32 fminimum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf32 (const _Float32 *__x, const _Float32 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf32 (const _Float32 *__x, const _Float32 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern _Float32 getpayloadf32 (const _Float32 *__x) noexcept (true); extern _Float32 __getpayloadf32 (const _Float32 *__x) noexcept (true);
+
+
+extern int setpayloadf32 (_Float32 *__x, _Float32 __payload) noexcept (true);
+
+
+extern int setpayloadsigf32 (_Float32 *__x, _Float32 __payload) noexcept (true);
+# 451 "/usr/include/math.h" 2 3 4
+# 467 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern _Float64 acosf64 (_Float64 __x) noexcept (true); extern _Float64 __acosf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 asinf64 (_Float64 __x) noexcept (true); extern _Float64 __asinf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 atanf64 (_Float64 __x) noexcept (true); extern _Float64 __atanf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 atan2f64 (_Float64 __y, _Float64 __x) noexcept (true); extern _Float64 __atan2f64 (_Float64 __y, _Float64 __x) noexcept (true);
+
+
+ extern _Float64 cosf64 (_Float64 __x) noexcept (true); extern _Float64 __cosf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 sinf64 (_Float64 __x) noexcept (true); extern _Float64 __sinf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 tanf64 (_Float64 __x) noexcept (true); extern _Float64 __tanf64 (_Float64 __x) noexcept (true);
+
+
+
+
+ extern _Float64 coshf64 (_Float64 __x) noexcept (true); extern _Float64 __coshf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 sinhf64 (_Float64 __x) noexcept (true); extern _Float64 __sinhf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 tanhf64 (_Float64 __x) noexcept (true); extern _Float64 __tanhf64 (_Float64 __x) noexcept (true);
+
+
+
+ extern void sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) noexcept (true); extern void __sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern _Float64 acoshf64 (_Float64 __x) noexcept (true); extern _Float64 __acoshf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 asinhf64 (_Float64 __x) noexcept (true); extern _Float64 __asinhf64 (_Float64 __x) noexcept (true);
+
+ extern _Float64 atanhf64 (_Float64 __x) noexcept (true); extern _Float64 __atanhf64 (_Float64 __x) noexcept (true);
+
+
+
+
+
+ extern _Float64 expf64 (_Float64 __x) noexcept (true); extern _Float64 __expf64 (_Float64 __x) noexcept (true);
+
+
+extern _Float64 frexpf64 (_Float64 __x, int *__exponent) noexcept (true); extern _Float64 __frexpf64 (_Float64 __x, int *__exponent) noexcept (true);
+
+
+extern _Float64 ldexpf64 (_Float64 __x, int __exponent) noexcept (true); extern _Float64 __ldexpf64 (_Float64 __x, int __exponent) noexcept (true);
+
+
+ extern _Float64 logf64 (_Float64 __x) noexcept (true); extern _Float64 __logf64 (_Float64 __x) noexcept (true);
+
+
+ extern _Float64 log10f64 (_Float64 __x) noexcept (true); extern _Float64 __log10f64 (_Float64 __x) noexcept (true);
+
+
+extern _Float64 modff64 (_Float64 __x, _Float64 *__iptr) noexcept (true); extern _Float64 __modff64 (_Float64 __x, _Float64 *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern _Float64 exp10f64 (_Float64 __x) noexcept (true); extern _Float64 __exp10f64 (_Float64 __x) noexcept (true);
+
+
+
+
+ extern _Float64 expm1f64 (_Float64 __x) noexcept (true); extern _Float64 __expm1f64 (_Float64 __x) noexcept (true);
+
+
+ extern _Float64 log1pf64 (_Float64 __x) noexcept (true); extern _Float64 __log1pf64 (_Float64 __x) noexcept (true);
+
+
+extern _Float64 logbf64 (_Float64 __x) noexcept (true); extern _Float64 __logbf64 (_Float64 __x) noexcept (true);
+
+
+
+
+ extern _Float64 exp2f64 (_Float64 __x) noexcept (true); extern _Float64 __exp2f64 (_Float64 __x) noexcept (true);
+
+
+ extern _Float64 log2f64 (_Float64 __x) noexcept (true); extern _Float64 __log2f64 (_Float64 __x) noexcept (true);
+
+
+
+
+
+
+ extern _Float64 powf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __powf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float64 sqrtf64 (_Float64 __x) noexcept (true); extern _Float64 __sqrtf64 (_Float64 __x) noexcept (true);
+
+
+
+ extern _Float64 hypotf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __hypotf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+
+
+ extern _Float64 cbrtf64 (_Float64 __x) noexcept (true); extern _Float64 __cbrtf64 (_Float64 __x) noexcept (true);
+
+
+
+
+
+
+extern _Float64 ceilf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __ceilf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fabsf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fabsf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 floorf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __floorf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fmodf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __fmodf64 (_Float64 __x, _Float64 __y) noexcept (true);
+# 198 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64 copysignf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __copysignf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64 nanf64 (const char *__tagb) noexcept (true); extern _Float64 __nanf64 (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64 j0f64 (_Float64) noexcept (true); extern _Float64 __j0f64 (_Float64) noexcept (true);
+extern _Float64 j1f64 (_Float64) noexcept (true); extern _Float64 __j1f64 (_Float64) noexcept (true);
+extern _Float64 jnf64 (int, _Float64) noexcept (true); extern _Float64 __jnf64 (int, _Float64) noexcept (true);
+extern _Float64 y0f64 (_Float64) noexcept (true); extern _Float64 __y0f64 (_Float64) noexcept (true);
+extern _Float64 y1f64 (_Float64) noexcept (true); extern _Float64 __y1f64 (_Float64) noexcept (true);
+extern _Float64 ynf64 (int, _Float64) noexcept (true); extern _Float64 __ynf64 (int, _Float64) noexcept (true);
+
+
+
+
+
+ extern _Float64 erff64 (_Float64) noexcept (true); extern _Float64 __erff64 (_Float64) noexcept (true);
+ extern _Float64 erfcf64 (_Float64) noexcept (true); extern _Float64 __erfcf64 (_Float64) noexcept (true);
+extern _Float64 lgammaf64 (_Float64) noexcept (true); extern _Float64 __lgammaf64 (_Float64) noexcept (true);
+
+
+
+
+extern _Float64 tgammaf64 (_Float64) noexcept (true); extern _Float64 __tgammaf64 (_Float64) noexcept (true);
+# 252 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64 lgammaf64_r (_Float64, int *__signgamp) noexcept (true); extern _Float64 __lgammaf64_r (_Float64, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern _Float64 rintf64 (_Float64 __x) noexcept (true); extern _Float64 __rintf64 (_Float64 __x) noexcept (true);
+
+
+extern _Float64 nextafterf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __nextafterf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+
+
+
+
+extern _Float64 nextdownf64 (_Float64 __x) noexcept (true); extern _Float64 __nextdownf64 (_Float64 __x) noexcept (true);
+
+extern _Float64 nextupf64 (_Float64 __x) noexcept (true); extern _Float64 __nextupf64 (_Float64 __x) noexcept (true);
+
+
+
+extern _Float64 remainderf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __remainderf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+
+extern _Float64 scalbnf64 (_Float64 __x, int __n) noexcept (true); extern _Float64 __scalbnf64 (_Float64 __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf64 (_Float64 __x) noexcept (true); extern int __ilogbf64 (_Float64 __x) noexcept (true);
+
+
+
+
+extern long int llogbf64 (_Float64 __x) noexcept (true); extern long int __llogbf64 (_Float64 __x) noexcept (true);
+
+
+
+
+extern _Float64 scalblnf64 (_Float64 __x, long int __n) noexcept (true); extern _Float64 __scalblnf64 (_Float64 __x, long int __n) noexcept (true);
+
+
+
+extern _Float64 nearbyintf64 (_Float64 __x) noexcept (true); extern _Float64 __nearbyintf64 (_Float64 __x) noexcept (true);
+
+
+
+extern _Float64 roundf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __roundf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float64 truncf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __truncf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64 remquof64 (_Float64 __x, _Float64 __y, int *__quo) noexcept (true); extern _Float64 __remquof64 (_Float64 __x, _Float64 __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf64 (_Float64 __x) noexcept (true); extern long int __lrintf64 (_Float64 __x) noexcept (true);
+__extension__
+extern long long int llrintf64 (_Float64 __x) noexcept (true); extern long long int __llrintf64 (_Float64 __x) noexcept (true);
+
+
+
+extern long int lroundf64 (_Float64 __x) noexcept (true); extern long int __lroundf64 (_Float64 __x) noexcept (true);
+__extension__
+extern long long int llroundf64 (_Float64 __x) noexcept (true); extern long long int __llroundf64 (_Float64 __x) noexcept (true);
+
+
+
+extern _Float64 fdimf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __fdimf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+
+extern _Float64 fmaxf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaxf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float64 fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true); extern _Float64 __fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);
+
+
+
+
+extern _Float64 roundevenf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __roundevenf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef64 (_Float64 *__cx, const _Float64 *__x) noexcept (true);
+
+
+
+
+
+
+extern _Float64 fmaxmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaxmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64 fmaximumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminimumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fmaximum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminimum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fmaximum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminimum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fmaximum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64 fminimum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf64 (const _Float64 *__x, const _Float64 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf64 (const _Float64 *__x, const _Float64 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern _Float64 getpayloadf64 (const _Float64 *__x) noexcept (true); extern _Float64 __getpayloadf64 (const _Float64 *__x) noexcept (true);
+
+
+extern int setpayloadf64 (_Float64 *__x, _Float64 __payload) noexcept (true);
+
+
+extern int setpayloadsigf64 (_Float64 *__x, _Float64 __payload) noexcept (true);
+# 468 "/usr/include/math.h" 2 3 4
+# 484 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern _Float128 acosf128 (_Float128 __x) noexcept (true); extern _Float128 __acosf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 asinf128 (_Float128 __x) noexcept (true); extern _Float128 __asinf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 atanf128 (_Float128 __x) noexcept (true); extern _Float128 __atanf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 atan2f128 (_Float128 __y, _Float128 __x) noexcept (true); extern _Float128 __atan2f128 (_Float128 __y, _Float128 __x) noexcept (true);
+
+
+ extern _Float128 cosf128 (_Float128 __x) noexcept (true); extern _Float128 __cosf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 sinf128 (_Float128 __x) noexcept (true); extern _Float128 __sinf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 tanf128 (_Float128 __x) noexcept (true); extern _Float128 __tanf128 (_Float128 __x) noexcept (true);
+
+
+
+
+ extern _Float128 coshf128 (_Float128 __x) noexcept (true); extern _Float128 __coshf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 sinhf128 (_Float128 __x) noexcept (true); extern _Float128 __sinhf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 tanhf128 (_Float128 __x) noexcept (true); extern _Float128 __tanhf128 (_Float128 __x) noexcept (true);
+
+
+
+ extern void sincosf128 (_Float128 __x, _Float128 *__sinx, _Float128 *__cosx) noexcept (true); extern void __sincosf128 (_Float128 __x, _Float128 *__sinx, _Float128 *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern _Float128 acoshf128 (_Float128 __x) noexcept (true); extern _Float128 __acoshf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 asinhf128 (_Float128 __x) noexcept (true); extern _Float128 __asinhf128 (_Float128 __x) noexcept (true);
+
+ extern _Float128 atanhf128 (_Float128 __x) noexcept (true); extern _Float128 __atanhf128 (_Float128 __x) noexcept (true);
+
+
+
+
+
+ extern _Float128 expf128 (_Float128 __x) noexcept (true); extern _Float128 __expf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float128 frexpf128 (_Float128 __x, int *__exponent) noexcept (true); extern _Float128 __frexpf128 (_Float128 __x, int *__exponent) noexcept (true);
+
+
+extern _Float128 ldexpf128 (_Float128 __x, int __exponent) noexcept (true); extern _Float128 __ldexpf128 (_Float128 __x, int __exponent) noexcept (true);
+
+
+ extern _Float128 logf128 (_Float128 __x) noexcept (true); extern _Float128 __logf128 (_Float128 __x) noexcept (true);
+
+
+ extern _Float128 log10f128 (_Float128 __x) noexcept (true); extern _Float128 __log10f128 (_Float128 __x) noexcept (true);
+
+
+extern _Float128 modff128 (_Float128 __x, _Float128 *__iptr) noexcept (true); extern _Float128 __modff128 (_Float128 __x, _Float128 *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern _Float128 exp10f128 (_Float128 __x) noexcept (true); extern _Float128 __exp10f128 (_Float128 __x) noexcept (true);
+
+
+
+
+ extern _Float128 expm1f128 (_Float128 __x) noexcept (true); extern _Float128 __expm1f128 (_Float128 __x) noexcept (true);
+
+
+ extern _Float128 log1pf128 (_Float128 __x) noexcept (true); extern _Float128 __log1pf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float128 logbf128 (_Float128 __x) noexcept (true); extern _Float128 __logbf128 (_Float128 __x) noexcept (true);
+
+
+
+
+ extern _Float128 exp2f128 (_Float128 __x) noexcept (true); extern _Float128 __exp2f128 (_Float128 __x) noexcept (true);
+
+
+ extern _Float128 log2f128 (_Float128 __x) noexcept (true); extern _Float128 __log2f128 (_Float128 __x) noexcept (true);
+
+
+
+
+
+
+ extern _Float128 powf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __powf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float128 sqrtf128 (_Float128 __x) noexcept (true); extern _Float128 __sqrtf128 (_Float128 __x) noexcept (true);
+
+
+
+ extern _Float128 hypotf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __hypotf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+
+
+ extern _Float128 cbrtf128 (_Float128 __x) noexcept (true); extern _Float128 __cbrtf128 (_Float128 __x) noexcept (true);
+
+
+
+
+
+
+extern _Float128 ceilf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __ceilf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fabsf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fabsf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 floorf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __floorf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fmodf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __fmodf128 (_Float128 __x, _Float128 __y) noexcept (true);
+# 198 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float128 copysignf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __copysignf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float128 nanf128 (const char *__tagb) noexcept (true); extern _Float128 __nanf128 (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float128 j0f128 (_Float128) noexcept (true); extern _Float128 __j0f128 (_Float128) noexcept (true);
+extern _Float128 j1f128 (_Float128) noexcept (true); extern _Float128 __j1f128 (_Float128) noexcept (true);
+extern _Float128 jnf128 (int, _Float128) noexcept (true); extern _Float128 __jnf128 (int, _Float128) noexcept (true);
+extern _Float128 y0f128 (_Float128) noexcept (true); extern _Float128 __y0f128 (_Float128) noexcept (true);
+extern _Float128 y1f128 (_Float128) noexcept (true); extern _Float128 __y1f128 (_Float128) noexcept (true);
+extern _Float128 ynf128 (int, _Float128) noexcept (true); extern _Float128 __ynf128 (int, _Float128) noexcept (true);
+
+
+
+
+
+ extern _Float128 erff128 (_Float128) noexcept (true); extern _Float128 __erff128 (_Float128) noexcept (true);
+ extern _Float128 erfcf128 (_Float128) noexcept (true); extern _Float128 __erfcf128 (_Float128) noexcept (true);
+extern _Float128 lgammaf128 (_Float128) noexcept (true); extern _Float128 __lgammaf128 (_Float128) noexcept (true);
+
+
+
+
+extern _Float128 tgammaf128 (_Float128) noexcept (true); extern _Float128 __tgammaf128 (_Float128) noexcept (true);
+# 252 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float128 lgammaf128_r (_Float128, int *__signgamp) noexcept (true); extern _Float128 __lgammaf128_r (_Float128, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern _Float128 rintf128 (_Float128 __x) noexcept (true); extern _Float128 __rintf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float128 nextafterf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __nextafterf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+
+
+
+
+extern _Float128 nextdownf128 (_Float128 __x) noexcept (true); extern _Float128 __nextdownf128 (_Float128 __x) noexcept (true);
+
+extern _Float128 nextupf128 (_Float128 __x) noexcept (true); extern _Float128 __nextupf128 (_Float128 __x) noexcept (true);
+
+
+
+extern _Float128 remainderf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __remainderf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+
+extern _Float128 scalbnf128 (_Float128 __x, int __n) noexcept (true); extern _Float128 __scalbnf128 (_Float128 __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf128 (_Float128 __x) noexcept (true); extern int __ilogbf128 (_Float128 __x) noexcept (true);
+
+
+
+
+extern long int llogbf128 (_Float128 __x) noexcept (true); extern long int __llogbf128 (_Float128 __x) noexcept (true);
+
+
+
+
+extern _Float128 scalblnf128 (_Float128 __x, long int __n) noexcept (true); extern _Float128 __scalblnf128 (_Float128 __x, long int __n) noexcept (true);
+
+
+
+extern _Float128 nearbyintf128 (_Float128 __x) noexcept (true); extern _Float128 __nearbyintf128 (_Float128 __x) noexcept (true);
+
+
+
+extern _Float128 roundf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __roundf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float128 truncf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __truncf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float128 remquof128 (_Float128 __x, _Float128 __y, int *__quo) noexcept (true); extern _Float128 __remquof128 (_Float128 __x, _Float128 __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf128 (_Float128 __x) noexcept (true); extern long int __lrintf128 (_Float128 __x) noexcept (true);
+__extension__
+extern long long int llrintf128 (_Float128 __x) noexcept (true); extern long long int __llrintf128 (_Float128 __x) noexcept (true);
+
+
+
+extern long int lroundf128 (_Float128 __x) noexcept (true); extern long int __lroundf128 (_Float128 __x) noexcept (true);
+__extension__
+extern long long int llroundf128 (_Float128 __x) noexcept (true); extern long long int __llroundf128 (_Float128 __x) noexcept (true);
+
+
+
+extern _Float128 fdimf128 (_Float128 __x, _Float128 __y) noexcept (true); extern _Float128 __fdimf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+
+extern _Float128 fmaxf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaxf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float128 fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true); extern _Float128 __fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true);
+
+
+
+
+extern _Float128 roundevenf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__)); extern _Float128 __roundevenf128 (_Float128 __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf128 (_Float128 __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef128 (_Float128 *__cx, const _Float128 *__x) noexcept (true);
+
+
+
+
+
+
+extern _Float128 fmaxmagf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaxmagf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminmagf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminmagf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float128 fmaximumf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaximumf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminimumf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminimumf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fmaximum_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaximum_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminimum_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminimum_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fmaximum_magf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaximum_magf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminimum_magf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminimum_magf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fmaximum_mag_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fmaximum_mag_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float128 fminimum_mag_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__)); extern _Float128 __fminimum_mag_numf128 (_Float128 __x, _Float128 __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf128 (const _Float128 *__x, const _Float128 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf128 (const _Float128 *__x, const _Float128 *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern _Float128 getpayloadf128 (const _Float128 *__x) noexcept (true); extern _Float128 __getpayloadf128 (const _Float128 *__x) noexcept (true);
+
+
+extern int setpayloadf128 (_Float128 *__x, _Float128 __payload) noexcept (true);
+
+
+extern int setpayloadsigf128 (_Float128 *__x, _Float128 __payload) noexcept (true);
+# 485 "/usr/include/math.h" 2 3 4
+# 501 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern _Float32x acosf32x (_Float32x __x) noexcept (true); extern _Float32x __acosf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x asinf32x (_Float32x __x) noexcept (true); extern _Float32x __asinf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x atanf32x (_Float32x __x) noexcept (true); extern _Float32x __atanf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x atan2f32x (_Float32x __y, _Float32x __x) noexcept (true); extern _Float32x __atan2f32x (_Float32x __y, _Float32x __x) noexcept (true);
+
+
+ extern _Float32x cosf32x (_Float32x __x) noexcept (true); extern _Float32x __cosf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x sinf32x (_Float32x __x) noexcept (true); extern _Float32x __sinf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x tanf32x (_Float32x __x) noexcept (true); extern _Float32x __tanf32x (_Float32x __x) noexcept (true);
+
+
+
+
+ extern _Float32x coshf32x (_Float32x __x) noexcept (true); extern _Float32x __coshf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x sinhf32x (_Float32x __x) noexcept (true); extern _Float32x __sinhf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x tanhf32x (_Float32x __x) noexcept (true); extern _Float32x __tanhf32x (_Float32x __x) noexcept (true);
+
+
+
+ extern void sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) noexcept (true); extern void __sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern _Float32x acoshf32x (_Float32x __x) noexcept (true); extern _Float32x __acoshf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x asinhf32x (_Float32x __x) noexcept (true); extern _Float32x __asinhf32x (_Float32x __x) noexcept (true);
+
+ extern _Float32x atanhf32x (_Float32x __x) noexcept (true); extern _Float32x __atanhf32x (_Float32x __x) noexcept (true);
+
+
+
+
+
+ extern _Float32x expf32x (_Float32x __x) noexcept (true); extern _Float32x __expf32x (_Float32x __x) noexcept (true);
+
+
+extern _Float32x frexpf32x (_Float32x __x, int *__exponent) noexcept (true); extern _Float32x __frexpf32x (_Float32x __x, int *__exponent) noexcept (true);
+
+
+extern _Float32x ldexpf32x (_Float32x __x, int __exponent) noexcept (true); extern _Float32x __ldexpf32x (_Float32x __x, int __exponent) noexcept (true);
+
+
+ extern _Float32x logf32x (_Float32x __x) noexcept (true); extern _Float32x __logf32x (_Float32x __x) noexcept (true);
+
+
+ extern _Float32x log10f32x (_Float32x __x) noexcept (true); extern _Float32x __log10f32x (_Float32x __x) noexcept (true);
+
+
+extern _Float32x modff32x (_Float32x __x, _Float32x *__iptr) noexcept (true); extern _Float32x __modff32x (_Float32x __x, _Float32x *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern _Float32x exp10f32x (_Float32x __x) noexcept (true); extern _Float32x __exp10f32x (_Float32x __x) noexcept (true);
+
+
+
+
+ extern _Float32x expm1f32x (_Float32x __x) noexcept (true); extern _Float32x __expm1f32x (_Float32x __x) noexcept (true);
+
+
+ extern _Float32x log1pf32x (_Float32x __x) noexcept (true); extern _Float32x __log1pf32x (_Float32x __x) noexcept (true);
+
+
+extern _Float32x logbf32x (_Float32x __x) noexcept (true); extern _Float32x __logbf32x (_Float32x __x) noexcept (true);
+
+
+
+
+ extern _Float32x exp2f32x (_Float32x __x) noexcept (true); extern _Float32x __exp2f32x (_Float32x __x) noexcept (true);
+
+
+ extern _Float32x log2f32x (_Float32x __x) noexcept (true); extern _Float32x __log2f32x (_Float32x __x) noexcept (true);
+
+
+
+
+
+
+ extern _Float32x powf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __powf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+extern _Float32x sqrtf32x (_Float32x __x) noexcept (true); extern _Float32x __sqrtf32x (_Float32x __x) noexcept (true);
+
+
+
+ extern _Float32x hypotf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __hypotf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+
+
+ extern _Float32x cbrtf32x (_Float32x __x) noexcept (true); extern _Float32x __cbrtf32x (_Float32x __x) noexcept (true);
+
+
+
+
+
+
+extern _Float32x ceilf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __ceilf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fabsf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fabsf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x floorf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __floorf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fmodf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __fmodf32x (_Float32x __x, _Float32x __y) noexcept (true);
+# 198 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32x copysignf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __copysignf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32x nanf32x (const char *__tagb) noexcept (true); extern _Float32x __nanf32x (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32x j0f32x (_Float32x) noexcept (true); extern _Float32x __j0f32x (_Float32x) noexcept (true);
+extern _Float32x j1f32x (_Float32x) noexcept (true); extern _Float32x __j1f32x (_Float32x) noexcept (true);
+extern _Float32x jnf32x (int, _Float32x) noexcept (true); extern _Float32x __jnf32x (int, _Float32x) noexcept (true);
+extern _Float32x y0f32x (_Float32x) noexcept (true); extern _Float32x __y0f32x (_Float32x) noexcept (true);
+extern _Float32x y1f32x (_Float32x) noexcept (true); extern _Float32x __y1f32x (_Float32x) noexcept (true);
+extern _Float32x ynf32x (int, _Float32x) noexcept (true); extern _Float32x __ynf32x (int, _Float32x) noexcept (true);
+
+
+
+
+
+ extern _Float32x erff32x (_Float32x) noexcept (true); extern _Float32x __erff32x (_Float32x) noexcept (true);
+ extern _Float32x erfcf32x (_Float32x) noexcept (true); extern _Float32x __erfcf32x (_Float32x) noexcept (true);
+extern _Float32x lgammaf32x (_Float32x) noexcept (true); extern _Float32x __lgammaf32x (_Float32x) noexcept (true);
+
+
+
+
+extern _Float32x tgammaf32x (_Float32x) noexcept (true); extern _Float32x __tgammaf32x (_Float32x) noexcept (true);
+# 252 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float32x lgammaf32x_r (_Float32x, int *__signgamp) noexcept (true); extern _Float32x __lgammaf32x_r (_Float32x, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern _Float32x rintf32x (_Float32x __x) noexcept (true); extern _Float32x __rintf32x (_Float32x __x) noexcept (true);
+
+
+extern _Float32x nextafterf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __nextafterf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+
+
+
+
+extern _Float32x nextdownf32x (_Float32x __x) noexcept (true); extern _Float32x __nextdownf32x (_Float32x __x) noexcept (true);
+
+extern _Float32x nextupf32x (_Float32x __x) noexcept (true); extern _Float32x __nextupf32x (_Float32x __x) noexcept (true);
+
+
+
+extern _Float32x remainderf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __remainderf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+
+extern _Float32x scalbnf32x (_Float32x __x, int __n) noexcept (true); extern _Float32x __scalbnf32x (_Float32x __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf32x (_Float32x __x) noexcept (true); extern int __ilogbf32x (_Float32x __x) noexcept (true);
+
+
+
+
+extern long int llogbf32x (_Float32x __x) noexcept (true); extern long int __llogbf32x (_Float32x __x) noexcept (true);
+
+
+
+
+extern _Float32x scalblnf32x (_Float32x __x, long int __n) noexcept (true); extern _Float32x __scalblnf32x (_Float32x __x, long int __n) noexcept (true);
+
+
+
+extern _Float32x nearbyintf32x (_Float32x __x) noexcept (true); extern _Float32x __nearbyintf32x (_Float32x __x) noexcept (true);
+
+
+
+extern _Float32x roundf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __roundf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float32x truncf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __truncf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32x remquof32x (_Float32x __x, _Float32x __y, int *__quo) noexcept (true); extern _Float32x __remquof32x (_Float32x __x, _Float32x __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf32x (_Float32x __x) noexcept (true); extern long int __lrintf32x (_Float32x __x) noexcept (true);
+__extension__
+extern long long int llrintf32x (_Float32x __x) noexcept (true); extern long long int __llrintf32x (_Float32x __x) noexcept (true);
+
+
+
+extern long int lroundf32x (_Float32x __x) noexcept (true); extern long int __lroundf32x (_Float32x __x) noexcept (true);
+__extension__
+extern long long int llroundf32x (_Float32x __x) noexcept (true); extern long long int __llroundf32x (_Float32x __x) noexcept (true);
+
+
+
+extern _Float32x fdimf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __fdimf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+
+extern _Float32x fmaxf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaxf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float32x fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true); extern _Float32x __fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true);
+
+
+
+
+extern _Float32x roundevenf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __roundevenf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef32x (_Float32x *__cx, const _Float32x *__x) noexcept (true);
+
+
+
+
+
+
+extern _Float32x fmaxmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaxmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float32x fmaximumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminimumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fmaximum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminimum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fmaximum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminimum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fmaximum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float32x fminimum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf32x (const _Float32x *__x, const _Float32x *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf32x (const _Float32x *__x, const _Float32x *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern _Float32x getpayloadf32x (const _Float32x *__x) noexcept (true); extern _Float32x __getpayloadf32x (const _Float32x *__x) noexcept (true);
+
+
+extern int setpayloadf32x (_Float32x *__x, _Float32x __payload) noexcept (true);
+
+
+extern int setpayloadsigf32x (_Float32x *__x, _Float32x __payload) noexcept (true);
+# 502 "/usr/include/math.h" 2 3 4
+# 518 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 1 3 4
+# 53 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+ extern _Float64x acosf64x (_Float64x __x) noexcept (true); extern _Float64x __acosf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x asinf64x (_Float64x __x) noexcept (true); extern _Float64x __asinf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x atanf64x (_Float64x __x) noexcept (true); extern _Float64x __atanf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x atan2f64x (_Float64x __y, _Float64x __x) noexcept (true); extern _Float64x __atan2f64x (_Float64x __y, _Float64x __x) noexcept (true);
+
+
+ extern _Float64x cosf64x (_Float64x __x) noexcept (true); extern _Float64x __cosf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x sinf64x (_Float64x __x) noexcept (true); extern _Float64x __sinf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x tanf64x (_Float64x __x) noexcept (true); extern _Float64x __tanf64x (_Float64x __x) noexcept (true);
+
+
+
+
+ extern _Float64x coshf64x (_Float64x __x) noexcept (true); extern _Float64x __coshf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x sinhf64x (_Float64x __x) noexcept (true); extern _Float64x __sinhf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x tanhf64x (_Float64x __x) noexcept (true); extern _Float64x __tanhf64x (_Float64x __x) noexcept (true);
+
+
+
+ extern void sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) noexcept (true); extern void __sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) noexcept (true)
+                                                        ;
+
+
+
+
+ extern _Float64x acoshf64x (_Float64x __x) noexcept (true); extern _Float64x __acoshf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x asinhf64x (_Float64x __x) noexcept (true); extern _Float64x __asinhf64x (_Float64x __x) noexcept (true);
+
+ extern _Float64x atanhf64x (_Float64x __x) noexcept (true); extern _Float64x __atanhf64x (_Float64x __x) noexcept (true);
+
+
+
+
+
+ extern _Float64x expf64x (_Float64x __x) noexcept (true); extern _Float64x __expf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float64x frexpf64x (_Float64x __x, int *__exponent) noexcept (true); extern _Float64x __frexpf64x (_Float64x __x, int *__exponent) noexcept (true);
+
+
+extern _Float64x ldexpf64x (_Float64x __x, int __exponent) noexcept (true); extern _Float64x __ldexpf64x (_Float64x __x, int __exponent) noexcept (true);
+
+
+ extern _Float64x logf64x (_Float64x __x) noexcept (true); extern _Float64x __logf64x (_Float64x __x) noexcept (true);
+
+
+ extern _Float64x log10f64x (_Float64x __x) noexcept (true); extern _Float64x __log10f64x (_Float64x __x) noexcept (true);
+
+
+extern _Float64x modff64x (_Float64x __x, _Float64x *__iptr) noexcept (true); extern _Float64x __modff64x (_Float64x __x, _Float64x *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+ extern _Float64x exp10f64x (_Float64x __x) noexcept (true); extern _Float64x __exp10f64x (_Float64x __x) noexcept (true);
+
+
+
+
+ extern _Float64x expm1f64x (_Float64x __x) noexcept (true); extern _Float64x __expm1f64x (_Float64x __x) noexcept (true);
+
+
+ extern _Float64x log1pf64x (_Float64x __x) noexcept (true); extern _Float64x __log1pf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float64x logbf64x (_Float64x __x) noexcept (true); extern _Float64x __logbf64x (_Float64x __x) noexcept (true);
+
+
+
+
+ extern _Float64x exp2f64x (_Float64x __x) noexcept (true); extern _Float64x __exp2f64x (_Float64x __x) noexcept (true);
+
+
+ extern _Float64x log2f64x (_Float64x __x) noexcept (true); extern _Float64x __log2f64x (_Float64x __x) noexcept (true);
+
+
+
+
+
+
+ extern _Float64x powf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __powf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float64x sqrtf64x (_Float64x __x) noexcept (true); extern _Float64x __sqrtf64x (_Float64x __x) noexcept (true);
+
+
+
+ extern _Float64x hypotf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __hypotf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+
+
+ extern _Float64x cbrtf64x (_Float64x __x) noexcept (true); extern _Float64x __cbrtf64x (_Float64x __x) noexcept (true);
+
+
+
+
+
+
+extern _Float64x ceilf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __ceilf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fabsf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fabsf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x floorf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __floorf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fmodf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __fmodf64x (_Float64x __x, _Float64x __y) noexcept (true);
+# 198 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64x copysignf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __copysignf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64x nanf64x (const char *__tagb) noexcept (true); extern _Float64x __nanf64x (const char *__tagb) noexcept (true);
+# 220 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64x j0f64x (_Float64x) noexcept (true); extern _Float64x __j0f64x (_Float64x) noexcept (true);
+extern _Float64x j1f64x (_Float64x) noexcept (true); extern _Float64x __j1f64x (_Float64x) noexcept (true);
+extern _Float64x jnf64x (int, _Float64x) noexcept (true); extern _Float64x __jnf64x (int, _Float64x) noexcept (true);
+extern _Float64x y0f64x (_Float64x) noexcept (true); extern _Float64x __y0f64x (_Float64x) noexcept (true);
+extern _Float64x y1f64x (_Float64x) noexcept (true); extern _Float64x __y1f64x (_Float64x) noexcept (true);
+extern _Float64x ynf64x (int, _Float64x) noexcept (true); extern _Float64x __ynf64x (int, _Float64x) noexcept (true);
+
+
+
+
+
+ extern _Float64x erff64x (_Float64x) noexcept (true); extern _Float64x __erff64x (_Float64x) noexcept (true);
+ extern _Float64x erfcf64x (_Float64x) noexcept (true); extern _Float64x __erfcf64x (_Float64x) noexcept (true);
+extern _Float64x lgammaf64x (_Float64x) noexcept (true); extern _Float64x __lgammaf64x (_Float64x) noexcept (true);
+
+
+
+
+extern _Float64x tgammaf64x (_Float64x) noexcept (true); extern _Float64x __tgammaf64x (_Float64x) noexcept (true);
+# 252 "/usr/include/aarch64-linux-gnu/bits/mathcalls.h" 3 4
+extern _Float64x lgammaf64x_r (_Float64x, int *__signgamp) noexcept (true); extern _Float64x __lgammaf64x_r (_Float64x, int *__signgamp) noexcept (true);
+
+
+
+
+
+
+extern _Float64x rintf64x (_Float64x __x) noexcept (true); extern _Float64x __rintf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float64x nextafterf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __nextafterf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+
+
+
+
+extern _Float64x nextdownf64x (_Float64x __x) noexcept (true); extern _Float64x __nextdownf64x (_Float64x __x) noexcept (true);
+
+extern _Float64x nextupf64x (_Float64x __x) noexcept (true); extern _Float64x __nextupf64x (_Float64x __x) noexcept (true);
+
+
+
+extern _Float64x remainderf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __remainderf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+
+extern _Float64x scalbnf64x (_Float64x __x, int __n) noexcept (true); extern _Float64x __scalbnf64x (_Float64x __x, int __n) noexcept (true);
+
+
+
+extern int ilogbf64x (_Float64x __x) noexcept (true); extern int __ilogbf64x (_Float64x __x) noexcept (true);
+
+
+
+
+extern long int llogbf64x (_Float64x __x) noexcept (true); extern long int __llogbf64x (_Float64x __x) noexcept (true);
+
+
+
+
+extern _Float64x scalblnf64x (_Float64x __x, long int __n) noexcept (true); extern _Float64x __scalblnf64x (_Float64x __x, long int __n) noexcept (true);
+
+
+
+extern _Float64x nearbyintf64x (_Float64x __x) noexcept (true); extern _Float64x __nearbyintf64x (_Float64x __x) noexcept (true);
+
+
+
+extern _Float64x roundf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __roundf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float64x truncf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __truncf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64x remquof64x (_Float64x __x, _Float64x __y, int *__quo) noexcept (true); extern _Float64x __remquof64x (_Float64x __x, _Float64x __y, int *__quo) noexcept (true);
+
+
+
+
+
+
+extern long int lrintf64x (_Float64x __x) noexcept (true); extern long int __lrintf64x (_Float64x __x) noexcept (true);
+__extension__
+extern long long int llrintf64x (_Float64x __x) noexcept (true); extern long long int __llrintf64x (_Float64x __x) noexcept (true);
+
+
+
+extern long int lroundf64x (_Float64x __x) noexcept (true); extern long int __lroundf64x (_Float64x __x) noexcept (true);
+__extension__
+extern long long int llroundf64x (_Float64x __x) noexcept (true); extern long long int __llroundf64x (_Float64x __x) noexcept (true);
+
+
+
+extern _Float64x fdimf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __fdimf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+
+extern _Float64x fmaxf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaxf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern _Float64x fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true); extern _Float64x __fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);
+
+
+
+
+extern _Float64x roundevenf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __roundevenf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));
+
+
+
+extern __intmax_t fromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true)
+                            ;
+
+
+
+extern __uintmax_t ufromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true)
+                              ;
+
+
+
+
+extern __intmax_t fromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true)
+                             ;
+
+
+
+
+extern __uintmax_t ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true)
+                               ;
+
+
+extern int canonicalizef64x (_Float64x *__cx, const _Float64x *__x) noexcept (true);
+
+
+
+
+
+
+extern _Float64x fmaxmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaxmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern _Float64x fmaximumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminimumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fmaximum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminimum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fmaximum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminimum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fmaximum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+extern _Float64x fminimum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+extern int totalorderf64x (const _Float64x *__x, const _Float64x *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern int totalordermagf64x (const _Float64x *__x, const _Float64x *__y) noexcept (true)
+
+     __attribute__ ((__pure__));
+
+
+extern _Float64x getpayloadf64x (const _Float64x *__x) noexcept (true); extern _Float64x __getpayloadf64x (const _Float64x *__x) noexcept (true);
+
+
+extern int setpayloadf64x (_Float64x *__x, _Float64x __payload) noexcept (true);
+
+
+extern int setpayloadsigf64x (_Float64x *__x, _Float64x __payload) noexcept (true);
+# 519 "/usr/include/math.h" 2 3 4
+# 566 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern float fadd (double __x, double __y) noexcept (true);
+
+
+extern float fdiv (double __x, double __y) noexcept (true);
+
+
+extern float ffma (double __x, double __y, double __z) noexcept (true);
+
+
+extern float fmul (double __x, double __y) noexcept (true);
+
+
+extern float fsqrt (double __x) noexcept (true);
+
+
+extern float fsub (double __x, double __y) noexcept (true);
+# 567 "/usr/include/math.h" 2 3 4
+# 587 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern float faddl (long double __x, long double __y) noexcept (true);
+
+
+extern float fdivl (long double __x, long double __y) noexcept (true);
+
+
+extern float ffmal (long double __x, long double __y, long double __z) noexcept (true);
+
+
+extern float fmull (long double __x, long double __y) noexcept (true);
+
+
+extern float fsqrtl (long double __x) noexcept (true);
+
+
+extern float fsubl (long double __x, long double __y) noexcept (true);
+# 588 "/usr/include/math.h" 2 3 4
+# 616 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern double daddl (long double __x, long double __y) noexcept (true);
+
+
+extern double ddivl (long double __x, long double __y) noexcept (true);
+
+
+extern double dfmal (long double __x, long double __y, long double __z) noexcept (true);
+
+
+extern double dmull (long double __x, long double __y) noexcept (true);
+
+
+extern double dsqrtl (long double __x) noexcept (true);
+
+
+extern double dsubl (long double __x, long double __y) noexcept (true);
+# 617 "/usr/include/math.h" 2 3 4
+# 697 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32 f32addf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+extern _Float32 f32divf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+extern _Float32 f32fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true);
+
+
+extern _Float32 f32mulf32x (_Float32x __x, _Float32x __y) noexcept (true);
+
+
+extern _Float32 f32sqrtf32x (_Float32x __x) noexcept (true);
+
+
+extern _Float32 f32subf32x (_Float32x __x, _Float32x __y) noexcept (true);
+# 698 "/usr/include/math.h" 2 3 4
+# 707 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32 f32addf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32 f32divf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32 f32fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);
+
+
+extern _Float32 f32mulf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32 f32sqrtf64 (_Float64 __x) noexcept (true);
+
+
+extern _Float32 f32subf64 (_Float64 __x, _Float64 __y) noexcept (true);
+# 708 "/usr/include/math.h" 2 3 4
+# 717 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32 f32addf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32 f32divf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32 f32fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);
+
+
+extern _Float32 f32mulf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32 f32sqrtf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float32 f32subf64x (_Float64x __x, _Float64x __y) noexcept (true);
+# 718 "/usr/include/math.h" 2 3 4
+# 727 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32 f32addf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32 f32divf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32 f32fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true);
+
+
+extern _Float32 f32mulf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32 f32sqrtf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float32 f32subf128 (_Float128 __x, _Float128 __y) noexcept (true);
+# 728 "/usr/include/math.h" 2 3 4
+# 747 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32x f32xaddf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32x f32xdivf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32x f32xfmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);
+
+
+extern _Float32x f32xmulf64 (_Float64 __x, _Float64 __y) noexcept (true);
+
+
+extern _Float32x f32xsqrtf64 (_Float64 __x) noexcept (true);
+
+
+extern _Float32x f32xsubf64 (_Float64 __x, _Float64 __y) noexcept (true);
+# 748 "/usr/include/math.h" 2 3 4
+# 757 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32x f32xaddf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32x f32xdivf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32x f32xfmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);
+
+
+extern _Float32x f32xmulf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float32x f32xsqrtf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float32x f32xsubf64x (_Float64x __x, _Float64x __y) noexcept (true);
+# 758 "/usr/include/math.h" 2 3 4
+# 767 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float32x f32xaddf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32x f32xdivf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32x f32xfmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true);
+
+
+extern _Float32x f32xmulf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float32x f32xsqrtf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float32x f32xsubf128 (_Float128 __x, _Float128 __y) noexcept (true);
+# 768 "/usr/include/math.h" 2 3 4
+# 787 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float64 f64addf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float64 f64divf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float64 f64fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);
+
+
+extern _Float64 f64mulf64x (_Float64x __x, _Float64x __y) noexcept (true);
+
+
+extern _Float64 f64sqrtf64x (_Float64x __x) noexcept (true);
+
+
+extern _Float64 f64subf64x (_Float64x __x, _Float64x __y) noexcept (true);
+# 788 "/usr/include/math.h" 2 3 4
+# 797 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float64 f64addf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64 f64divf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64 f64fmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true);
+
+
+extern _Float64 f64mulf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64 f64sqrtf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float64 f64subf128 (_Float128 __x, _Float128 __y) noexcept (true);
+# 798 "/usr/include/math.h" 2 3 4
+# 817 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/mathcalls-narrow.h" 3 4
+extern _Float64x f64xaddf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64x f64xdivf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64x f64xfmaf128 (_Float128 __x, _Float128 __y, _Float128 __z) noexcept (true);
+
+
+extern _Float64x f64xmulf128 (_Float128 __x, _Float128 __y) noexcept (true);
+
+
+extern _Float64x f64xsqrtf128 (_Float128 __x) noexcept (true);
+
+
+extern _Float64x f64xsubf128 (_Float128 __x, _Float128 __y) noexcept (true);
+# 818 "/usr/include/math.h" 2 3 4
+# 854 "/usr/include/math.h" 3 4
+extern int signgam;
+# 934 "/usr/include/math.h" 3 4
+enum
+  {
+    FP_NAN =
+
+      0,
+    FP_INFINITE =
+
+      1,
+    FP_ZERO =
+
+      2,
+    FP_SUBNORMAL =
+
+      3,
+    FP_NORMAL =
+
+      4
+  };
+# 1055 "/usr/include/math.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/iscanonical.h" 1 3 4
+# 1056 "/usr/include/math.h" 2 3 4
+# 1067 "/usr/include/math.h" 3 4
+extern "C++" {
+inline int issignaling (float __val) { return __issignalingf (__val); }
+inline int issignaling (double __val) { return __issignaling (__val); }
+inline int
+issignaling (long double __val)
+{
+
+
+
+  return __issignalingl (__val);
+
+}
+
+
+
+
+
+}
+# 1098 "/usr/include/math.h" 3 4
+extern "C++" {
+# 1129 "/usr/include/math.h" 3 4
+template <class __T> inline bool
+iszero (__T __val)
+{
+  return __val == 0;
+}
+
+}
+# 1364 "/usr/include/math.h" 3 4
+extern "C++" {
+template<typename> struct __iseqsig_type;
+
+template<> struct __iseqsig_type<float>
+{
+  static int __call (float __x, float __y) throw ()
+  {
+    return __iseqsigf (__x, __y);
+  }
+};
+
+template<> struct __iseqsig_type<double>
+{
+  static int __call (double __x, double __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+
+template<> struct __iseqsig_type<long double>
+{
+  static int __call (long double __x, long double __y) throw ()
+  {
+
+    return __iseqsigl (__x, __y);
+
+
+
+  }
+};
+
+
+template<> struct __iseqsig_type<_Float32>
+{
+  static int __call (_Float32 __x, _Float32 __y) throw ()
+  {
+    return __iseqsigf (__x, __y);
+  }
+};
+
+
+
+template<> struct __iseqsig_type<_Float64>
+{
+  static int __call (_Float64 __x, _Float64 __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+
+
+
+
+
+template<> struct __iseqsig_type<_Float128>
+{
+  static int __call (_Float128 __x, _Float128 __y) throw ()
+  {
+
+
+
+    return __iseqsigl (__x, __y);
+
+  }
+};
+
+
+
+template<> struct __iseqsig_type<_Float32x>
+{
+  static int __call (_Float32x __x, _Float32x __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+
+
+
+template<> struct __iseqsig_type<_Float64x>
+{
+  static int __call (_Float64x __x, _Float64x __y) throw ()
+  {
+
+    return __iseqsigl (__x, __y);
+
+
+
+  }
+};
+
+
+template<typename _T1, typename _T2>
+inline int
+iseqsig (_T1 __x, _T2 __y) throw ()
+{
+
+  typedef decltype (((__x) + (__y) + 0.0f)) _T3;
+
+
+
+  return __iseqsig_type<_T3>::__call (__x, __y);
+}
+
+}
+
+
+
+
+}
+# 48 "/usr/include/c++/13/cmath" 2 3
+
+# 1 "/usr/include/c++/13/bits/std_abs.h" 1 3
+# 33 "/usr/include/c++/13/bits/std_abs.h" 3
+       
+# 34 "/usr/include/c++/13/bits/std_abs.h" 3
+
+
+
+
+# 1 "/usr/include/stdlib.h" 1 3 4
+# 26 "/usr/include/stdlib.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
+# 27 "/usr/include/stdlib.h" 2 3 4
+
+
+
+
+
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 1 3 4
+# 214 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 3 4
+typedef long unsigned int size_t;
+# 33 "/usr/include/stdlib.h" 2 3 4
+
+extern "C" {
+
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/waitflags.h" 1 3 4
+# 41 "/usr/include/stdlib.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/waitstatus.h" 1 3 4
+# 42 "/usr/include/stdlib.h" 2 3 4
+# 59 "/usr/include/stdlib.h" 3 4
+typedef struct
+  {
+    int quot;
+    int rem;
+  } div_t;
+
+
+
+typedef struct
+  {
+    long int quot;
+    long int rem;
+  } ldiv_t;
+
+
+
+
+
+__extension__ typedef struct
+  {
+    long long int quot;
+    long long int rem;
+  } lldiv_t;
+# 98 "/usr/include/stdlib.h" 3 4
+extern size_t __ctype_get_mb_cur_max (void) noexcept (true) ;
+
+
+
+extern double atof (const char *__nptr)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
+
+extern int atoi (const char *__nptr)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
+
+extern long int atol (const char *__nptr)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+__extension__ extern long long int atoll (const char *__nptr)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+extern double strtod (const char *__restrict __nptr,
+        char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern float strtof (const char *__restrict __nptr,
+       char **__restrict __endptr) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+extern long double strtold (const char *__restrict __nptr,
+       char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+# 141 "/usr/include/stdlib.h" 3 4
+extern _Float32 strtof32 (const char *__restrict __nptr,
+     char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern _Float64 strtof64 (const char *__restrict __nptr,
+     char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern _Float128 strtof128 (const char *__restrict __nptr,
+       char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern _Float32x strtof32x (const char *__restrict __nptr,
+       char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern _Float64x strtof64x (const char *__restrict __nptr,
+       char **__restrict __endptr)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+# 177 "/usr/include/stdlib.h" 3 4
+extern long int strtol (const char *__restrict __nptr,
+   char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+extern unsigned long int strtoul (const char *__restrict __nptr,
+      char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+__extension__
+extern long long int strtoq (const char *__restrict __nptr,
+        char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+__extension__
+extern unsigned long long int strtouq (const char *__restrict __nptr,
+           char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+__extension__
+extern long long int strtoll (const char *__restrict __nptr,
+         char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+__extension__
+extern unsigned long long int strtoull (const char *__restrict __nptr,
+     char **__restrict __endptr, int __base)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+
+extern long int strtol (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtol")
+
+
+     __attribute__ ((__nonnull__ (1)));
+extern unsigned long int strtoul (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtoul")
+
+
+
+     __attribute__ ((__nonnull__ (1)));
+
+__extension__
+extern long long int strtoq (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtoll")
+
+
+     __attribute__ ((__nonnull__ (1)));
+__extension__
+extern unsigned long long int strtouq (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtoull")
+
+
+
+     __attribute__ ((__nonnull__ (1)));
+
+__extension__
+extern long long int strtoll (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtoll")
+
+
+     __attribute__ ((__nonnull__ (1)));
+__extension__
+extern unsigned long long int strtoull (const char *__restrict __nptr, char **__restrict __endptr, int __base) noexcept (true) __asm__ ("" "__isoc23_strtoull")
+
+
+
+     __attribute__ ((__nonnull__ (1)));
+# 278 "/usr/include/stdlib.h" 3 4
+extern int strfromd (char *__dest, size_t __size, const char *__format,
+       double __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+extern int strfromf (char *__dest, size_t __size, const char *__format,
+       float __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+extern int strfroml (char *__dest, size_t __size, const char *__format,
+       long double __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+# 298 "/usr/include/stdlib.h" 3 4
+extern int strfromf32 (char *__dest, size_t __size, const char * __format,
+         _Float32 __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+
+
+extern int strfromf64 (char *__dest, size_t __size, const char * __format,
+         _Float64 __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+
+
+extern int strfromf128 (char *__dest, size_t __size, const char * __format,
+   _Float128 __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+
+
+extern int strfromf32x (char *__dest, size_t __size, const char * __format,
+   _Float32x __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+
+
+
+extern int strfromf64x (char *__dest, size_t __size, const char * __format,
+   _Float64x __f)
+     noexcept (true) __attribute__ ((__nonnull__ (3)));
+# 338 "/usr/include/stdlib.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 1 3 4
+# 22 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/__locale_t.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/bits/types/__locale_t.h" 3 4
+struct __locale_struct
+{
+
+  struct __locale_data *__locales[13];
+
+
+  const unsigned short int *__ctype_b;
+  const int *__ctype_tolower;
+  const int *__ctype_toupper;
+
+
+  const char *__names[13];
+};
+
+typedef struct __locale_struct *__locale_t;
+# 23 "/usr/include/aarch64-linux-gnu/bits/types/locale_t.h" 2 3 4
+
+typedef __locale_t locale_t;
+# 339 "/usr/include/stdlib.h" 2 3 4
+
+extern long int strtol_l (const char *__restrict __nptr,
+     char **__restrict __endptr, int __base,
+     locale_t __loc) noexcept (true) __attribute__ ((__nonnull__ (1, 4)));
+
+extern unsigned long int strtoul_l (const char *__restrict __nptr,
+        char **__restrict __endptr,
+        int __base, locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));
+
+__extension__
+extern long long int strtoll_l (const char *__restrict __nptr,
+    char **__restrict __endptr, int __base,
+    locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));
+
+__extension__
+extern unsigned long long int strtoull_l (const char *__restrict __nptr,
+       char **__restrict __endptr,
+       int __base, locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));
+
+
+
+
+
+extern long int strtol_l (const char *__restrict __nptr, char **__restrict __endptr, int __base, locale_t __loc) noexcept (true) __asm__ ("" "__isoc23_strtol_l")
+
+
+
+     __attribute__ ((__nonnull__ (1, 4)));
+extern unsigned long int strtoul_l (const char *__restrict __nptr, char **__restrict __endptr, int __base, locale_t __loc) noexcept (true) __asm__ ("" "__isoc23_strtoul_l")
+
+
+
+
+     __attribute__ ((__nonnull__ (1, 4)));
+__extension__
+extern long long int strtoll_l (const char *__restrict __nptr, char **__restrict __endptr, int __base, locale_t __loc) noexcept (true) __asm__ ("" "__isoc23_strtoll_l")
+
+
+
+
+     __attribute__ ((__nonnull__ (1, 4)));
+__extension__
+extern unsigned long long int strtoull_l (const char *__restrict __nptr, char **__restrict __endptr, int __base, locale_t __loc) noexcept (true) __asm__ ("" "__isoc23_strtoull_l")
+
+
+
+
+     __attribute__ ((__nonnull__ (1, 4)));
+# 415 "/usr/include/stdlib.h" 3 4
+extern double strtod_l (const char *__restrict __nptr,
+   char **__restrict __endptr, locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+extern float strtof_l (const char *__restrict __nptr,
+         char **__restrict __endptr, locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+extern long double strtold_l (const char *__restrict __nptr,
+         char **__restrict __endptr,
+         locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+# 436 "/usr/include/stdlib.h" 3 4
+extern _Float32 strtof32_l (const char *__restrict __nptr,
+       char **__restrict __endptr,
+       locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+
+
+extern _Float64 strtof64_l (const char *__restrict __nptr,
+       char **__restrict __endptr,
+       locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+
+
+extern _Float128 strtof128_l (const char *__restrict __nptr,
+         char **__restrict __endptr,
+         locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+
+
+extern _Float32x strtof32x_l (const char *__restrict __nptr,
+         char **__restrict __endptr,
+         locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+
+
+
+extern _Float64x strtof64x_l (const char *__restrict __nptr,
+         char **__restrict __endptr,
+         locale_t __loc)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
+# 505 "/usr/include/stdlib.h" 3 4
+extern char *l64a (long int __n) noexcept (true) ;
+
+
+extern long int a64l (const char *__s)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/sys/types.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/sys/types.h" 3 4
+extern "C" {
+
+
+
+
+
+typedef __u_char u_char;
+typedef __u_short u_short;
+typedef __u_int u_int;
+typedef __u_long u_long;
+typedef __quad_t quad_t;
+typedef __u_quad_t u_quad_t;
+typedef __fsid_t fsid_t;
+
+
+typedef __loff_t loff_t;
+
+
+
+
+typedef __ino_t ino_t;
+
+
+
+
+
+
+typedef __ino64_t ino64_t;
+
+
+
+
+typedef __dev_t dev_t;
+
+
+
+
+typedef __gid_t gid_t;
+
+
+
+
+typedef __mode_t mode_t;
+
+
+
+
+typedef __nlink_t nlink_t;
+
+
+
+
+typedef __uid_t uid_t;
+
+
+
+
+
+typedef __off_t off_t;
+
+
+
+
+
+
+typedef __off64_t off64_t;
+
+
+
+
+typedef __pid_t pid_t;
+
+
+
+
+
+typedef __id_t id_t;
+
+
+
+
+typedef __ssize_t ssize_t;
+
+
+
+
+
+typedef __daddr_t daddr_t;
+typedef __caddr_t caddr_t;
+
+
+
+
+
+typedef __key_t key_t;
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/clock_t.h" 1 3 4
+
+
+
+
+
+
+typedef __clock_t clock_t;
+# 127 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/clockid_t.h" 1 3 4
+
+
+
+
+
+
+typedef __clockid_t clockid_t;
+# 129 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/time_t.h" 1 3 4
+# 10 "/usr/include/aarch64-linux-gnu/bits/types/time_t.h" 3 4
+typedef __time_t time_t;
+# 130 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/timer_t.h" 1 3 4
+
+
+
+
+
+
+typedef __timer_t timer_t;
+# 131 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+
+typedef __useconds_t useconds_t;
+
+
+
+typedef __suseconds_t suseconds_t;
+
+
+
+
+
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 1 3 4
+# 145 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+
+typedef unsigned long int ulong;
+typedef unsigned short int ushort;
+typedef unsigned int uint;
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/stdint-intn.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/stdint-intn.h" 3 4
+typedef __int8_t int8_t;
+typedef __int16_t int16_t;
+typedef __int32_t int32_t;
+typedef __int64_t int64_t;
+# 156 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+typedef __uint8_t u_int8_t;
+typedef __uint16_t u_int16_t;
+typedef __uint32_t u_int32_t;
+typedef __uint64_t u_int64_t;
+
+
+typedef int register_t __attribute__ ((__mode__ (__word__)));
+# 176 "/usr/include/aarch64-linux-gnu/sys/types.h" 3 4
+# 1 "/usr/include/endian.h" 1 3 4
+# 24 "/usr/include/endian.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/endian.h" 1 3 4
+# 35 "/usr/include/aarch64-linux-gnu/bits/endian.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/endianness.h" 1 3 4
+# 36 "/usr/include/aarch64-linux-gnu/bits/endian.h" 2 3 4
+# 25 "/usr/include/endian.h" 2 3 4
+# 35 "/usr/include/endian.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/byteswap.h" 1 3 4
+# 33 "/usr/include/aarch64-linux-gnu/bits/byteswap.h" 3 4
+static __inline __uint16_t
+__bswap_16 (__uint16_t __bsx)
+{
+
+  return __builtin_bswap16 (__bsx);
+
+
+
+}
+
+
+
+
+
+
+static __inline __uint32_t
+__bswap_32 (__uint32_t __bsx)
+{
+
+  return __builtin_bswap32 (__bsx);
+
+
+
+}
+# 69 "/usr/include/aarch64-linux-gnu/bits/byteswap.h" 3 4
+__extension__ static __inline __uint64_t
+__bswap_64 (__uint64_t __bsx)
+{
+
+  return __builtin_bswap64 (__bsx);
+
+
+
+}
+# 36 "/usr/include/endian.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/uintn-identity.h" 1 3 4
+# 32 "/usr/include/aarch64-linux-gnu/bits/uintn-identity.h" 3 4
+static __inline __uint16_t
+__uint16_identity (__uint16_t __x)
+{
+  return __x;
+}
+
+static __inline __uint32_t
+__uint32_identity (__uint32_t __x)
+{
+  return __x;
+}
+
+static __inline __uint64_t
+__uint64_identity (__uint64_t __x)
+{
+  return __x;
+}
+# 37 "/usr/include/endian.h" 2 3 4
+# 177 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+# 1 "/usr/include/aarch64-linux-gnu/sys/select.h" 1 3 4
+# 30 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/select.h" 1 3 4
+# 31 "/usr/include/aarch64-linux-gnu/sys/select.h" 2 3 4
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/sigset_t.h" 1 3 4
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/__sigset_t.h" 1 3 4
+
+
+
+
+typedef struct
+{
+  unsigned long int __val[(1024 / (8 * sizeof (unsigned long int)))];
+} __sigset_t;
+# 5 "/usr/include/aarch64-linux-gnu/bits/types/sigset_t.h" 2 3 4
+
+
+typedef __sigset_t sigset_t;
+# 34 "/usr/include/aarch64-linux-gnu/sys/select.h" 2 3 4
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/struct_timeval.h" 1 3 4
+
+
+
+
+
+
+
+struct timeval
+{
+
+
+
+
+  __time_t tv_sec;
+  __suseconds_t tv_usec;
+
+};
+# 38 "/usr/include/aarch64-linux-gnu/sys/select.h" 2 3 4
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/types/struct_timespec.h" 1 3 4
+# 11 "/usr/include/aarch64-linux-gnu/bits/types/struct_timespec.h" 3 4
+struct timespec
+{
+
+
+
+  __time_t tv_sec;
+
+
+
+
+  __syscall_slong_t tv_nsec;
+# 31 "/usr/include/aarch64-linux-gnu/bits/types/struct_timespec.h" 3 4
+};
+# 40 "/usr/include/aarch64-linux-gnu/sys/select.h" 2 3 4
+# 49 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+typedef long int __fd_mask;
+# 59 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+typedef struct
+  {
+
+
+
+    __fd_mask fds_bits[1024 / (8 * (int) sizeof (__fd_mask))];
+
+
+
+
+
+  } fd_set;
+
+
+
+
+
+
+typedef __fd_mask fd_mask;
+# 91 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+extern "C" {
+# 102 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+extern int select (int __nfds, fd_set *__restrict __readfds,
+     fd_set *__restrict __writefds,
+     fd_set *__restrict __exceptfds,
+     struct timeval *__restrict __timeout);
+# 127 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+extern int pselect (int __nfds, fd_set *__restrict __readfds,
+      fd_set *__restrict __writefds,
+      fd_set *__restrict __exceptfds,
+      const struct timespec *__restrict __timeout,
+      const __sigset_t *__restrict __sigmask);
+# 153 "/usr/include/aarch64-linux-gnu/sys/select.h" 3 4
+}
+# 180 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+
+
+
+typedef __blksize_t blksize_t;
+
+
+
+
+
+
+typedef __blkcnt_t blkcnt_t;
+
+
+
+typedef __fsblkcnt_t fsblkcnt_t;
+
+
+
+typedef __fsfilcnt_t fsfilcnt_t;
+# 219 "/usr/include/aarch64-linux-gnu/sys/types.h" 3 4
+typedef __blkcnt64_t blkcnt64_t;
+typedef __fsblkcnt64_t fsblkcnt64_t;
+typedef __fsfilcnt64_t fsfilcnt64_t;
+
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/pthreadtypes.h" 1 3 4
+# 23 "/usr/include/aarch64-linux-gnu/bits/pthreadtypes.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 1 3 4
+# 44 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/pthreadtypes-arch.h" 1 3 4
+# 45 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 2 3 4
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/atomic_wide_counter.h" 1 3 4
+# 25 "/usr/include/aarch64-linux-gnu/bits/atomic_wide_counter.h" 3 4
+typedef union
+{
+  __extension__ unsigned long long int __value64;
+  struct
+  {
+    unsigned int __low;
+    unsigned int __high;
+  } __value32;
+} __atomic_wide_counter;
+# 47 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 2 3 4
+
+
+
+
+typedef struct __pthread_internal_list
+{
+  struct __pthread_internal_list *__prev;
+  struct __pthread_internal_list *__next;
+} __pthread_list_t;
+
+typedef struct __pthread_internal_slist
+{
+  struct __pthread_internal_slist *__next;
+} __pthread_slist_t;
+# 76 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/struct_mutex.h" 1 3 4
+# 27 "/usr/include/aarch64-linux-gnu/bits/struct_mutex.h" 3 4
+struct __pthread_mutex_s
+{
+  int __lock ;
+  unsigned int __count;
+  int __owner;
+
+  unsigned int __nusers;
+# 58 "/usr/include/aarch64-linux-gnu/bits/struct_mutex.h" 3 4
+  int __kind;
+
+
+
+
+  int __spins;
+  __pthread_list_t __list;
+# 74 "/usr/include/aarch64-linux-gnu/bits/struct_mutex.h" 3 4
+};
+# 77 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 2 3 4
+# 89 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/struct_rwlock.h" 1 3 4
+# 23 "/usr/include/aarch64-linux-gnu/bits/struct_rwlock.h" 3 4
+struct __pthread_rwlock_arch_t
+{
+  unsigned int __readers;
+  unsigned int __writers;
+  unsigned int __wrphase_futex;
+  unsigned int __writers_futex;
+  unsigned int __pad3;
+  unsigned int __pad4;
+  int __cur_writer;
+  int __shared;
+  unsigned long int __pad1;
+  unsigned long int __pad2;
+  unsigned int __flags;
+};
+# 90 "/usr/include/aarch64-linux-gnu/bits/thread-shared-types.h" 2 3 4
+
+
+
+
+struct __pthread_cond_s
+{
+  __atomic_wide_counter __wseq;
+  __atomic_wide_counter __g1_start;
+  unsigned int __g_refs[2] ;
+  unsigned int __g_size[2];
+  unsigned int __g1_orig_size;
+  unsigned int __wrefs;
+  unsigned int __g_signals[2];
+};
+
+typedef unsigned int __tss_t;
+typedef unsigned long int __thrd_t;
+
+typedef struct
+{
+  int __data ;
+} __once_flag;
+# 24 "/usr/include/aarch64-linux-gnu/bits/pthreadtypes.h" 2 3 4
+
+
+
+typedef unsigned long int pthread_t;
+
+
+
+
+typedef union
+{
+  char __size[8];
+  int __align;
+} pthread_mutexattr_t;
+
+
+
+
+typedef union
+{
+  char __size[8];
+  int __align;
+} pthread_condattr_t;
+
+
+
+typedef unsigned int pthread_key_t;
+
+
+
+typedef int pthread_once_t;
+
+
+union pthread_attr_t
+{
+  char __size[64];
+  long int __align;
+};
+
+typedef union pthread_attr_t pthread_attr_t;
+
+
+
+
+typedef union
+{
+  struct __pthread_mutex_s __data;
+  char __size[48];
+  long int __align;
+} pthread_mutex_t;
+
+
+typedef union
+{
+  struct __pthread_cond_s __data;
+  char __size[48];
+  __extension__ long long int __align;
+} pthread_cond_t;
+
+
+
+
+
+typedef union
+{
+  struct __pthread_rwlock_arch_t __data;
+  char __size[56];
+  long int __align;
+} pthread_rwlock_t;
+
+typedef union
+{
+  char __size[8];
+  long int __align;
+} pthread_rwlockattr_t;
+
+
+
+
+
+typedef volatile int pthread_spinlock_t;
+
+
+
+
+typedef union
+{
+  char __size[32];
+  long int __align;
+} pthread_barrier_t;
+
+typedef union
+{
+  char __size[8];
+  int __align;
+} pthread_barrierattr_t;
+# 228 "/usr/include/aarch64-linux-gnu/sys/types.h" 2 3 4
+
+
+}
+# 515 "/usr/include/stdlib.h" 2 3 4
+
+
+
+
+
+
+extern long int random (void) noexcept (true);
+
+
+extern void srandom (unsigned int __seed) noexcept (true);
+
+
+
+
+
+extern char *initstate (unsigned int __seed, char *__statebuf,
+   size_t __statelen) noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+extern char *setstate (char *__statebuf) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+
+
+struct random_data
+  {
+    int32_t *fptr;
+    int32_t *rptr;
+    int32_t *state;
+    int rand_type;
+    int rand_deg;
+    int rand_sep;
+    int32_t *end_ptr;
+  };
+
+extern int random_r (struct random_data *__restrict __buf,
+       int32_t *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+extern int srandom_r (unsigned int __seed, struct random_data *__buf)
+     noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+extern int initstate_r (unsigned int __seed, char *__restrict __statebuf,
+   size_t __statelen,
+   struct random_data *__restrict __buf)
+     noexcept (true) __attribute__ ((__nonnull__ (2, 4)));
+
+extern int setstate_r (char *__restrict __statebuf,
+         struct random_data *__restrict __buf)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+
+extern int rand (void) noexcept (true);
+
+extern void srand (unsigned int __seed) noexcept (true);
+
+
+
+extern int rand_r (unsigned int *__seed) noexcept (true);
+
+
+
+
+
+
+
+extern double drand48 (void) noexcept (true);
+extern double erand48 (unsigned short int __xsubi[3]) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+extern long int lrand48 (void) noexcept (true);
+extern long int nrand48 (unsigned short int __xsubi[3])
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+extern long int mrand48 (void) noexcept (true);
+extern long int jrand48 (unsigned short int __xsubi[3])
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+extern void srand48 (long int __seedval) noexcept (true);
+extern unsigned short int *seed48 (unsigned short int __seed16v[3])
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+extern void lcong48 (unsigned short int __param[7]) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+struct drand48_data
+  {
+    unsigned short int __x[3];
+    unsigned short int __old_x[3];
+    unsigned short int __c;
+    unsigned short int __init;
+    __extension__ unsigned long long int __a;
+
+  };
+
+
+extern int drand48_r (struct drand48_data *__restrict __buffer,
+        double *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern int erand48_r (unsigned short int __xsubi[3],
+        struct drand48_data *__restrict __buffer,
+        double *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int lrand48_r (struct drand48_data *__restrict __buffer,
+        long int *__restrict __result)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern int nrand48_r (unsigned short int __xsubi[3],
+        struct drand48_data *__restrict __buffer,
+        long int *__restrict __result)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int mrand48_r (struct drand48_data *__restrict __buffer,
+        long int *__restrict __result)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern int jrand48_r (unsigned short int __xsubi[3],
+        struct drand48_data *__restrict __buffer,
+        long int *__restrict __result)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int srand48_r (long int __seedval, struct drand48_data *__buffer)
+     noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+extern int seed48_r (unsigned short int __seed16v[3],
+       struct drand48_data *__buffer) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+extern int lcong48_r (unsigned short int __param[7],
+        struct drand48_data *__buffer)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern __uint32_t arc4random (void)
+     noexcept (true) ;
+
+
+extern void arc4random_buf (void *__buf, size_t __size)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern __uint32_t arc4random_uniform (__uint32_t __upper_bound)
+     noexcept (true) ;
+
+
+
+
+extern void *malloc (size_t __size) noexcept (true) __attribute__ ((__malloc__))
+     __attribute__ ((__alloc_size__ (1))) ;
+
+extern void *calloc (size_t __nmemb, size_t __size)
+     noexcept (true) __attribute__ ((__malloc__)) __attribute__ ((__alloc_size__ (1, 2))) ;
+
+
+
+
+
+
+extern void *realloc (void *__ptr, size_t __size)
+     noexcept (true) __attribute__ ((__warn_unused_result__)) __attribute__ ((__alloc_size__ (2)));
+
+
+extern void free (void *__ptr) noexcept (true);
+
+
+
+
+
+
+
+extern void *reallocarray (void *__ptr, size_t __nmemb, size_t __size)
+     noexcept (true) __attribute__ ((__warn_unused_result__))
+     __attribute__ ((__alloc_size__ (2, 3)))
+    __attribute__ ((__malloc__ (__builtin_free, 1)));
+
+
+extern void *reallocarray (void *__ptr, size_t __nmemb, size_t __size)
+     noexcept (true) __attribute__ ((__malloc__ (reallocarray, 1)));
+
+
+
+# 1 "/usr/include/alloca.h" 1 3 4
+# 24 "/usr/include/alloca.h" 3 4
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 1 3 4
+# 25 "/usr/include/alloca.h" 2 3 4
+
+extern "C" {
+
+
+
+
+
+extern void *alloca (size_t __size) noexcept (true);
+
+
+
+
+
+}
+# 707 "/usr/include/stdlib.h" 2 3 4
+
+
+
+
+
+extern void *valloc (size_t __size) noexcept (true) __attribute__ ((__malloc__))
+     __attribute__ ((__alloc_size__ (1))) ;
+
+
+
+
+extern int posix_memalign (void **__memptr, size_t __alignment, size_t __size)
+     noexcept (true) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+
+extern void *aligned_alloc (size_t __alignment, size_t __size)
+     noexcept (true) __attribute__ ((__malloc__)) __attribute__ ((__alloc_align__ (1)))
+     __attribute__ ((__alloc_size__ (2))) ;
+
+
+
+extern void abort (void) noexcept (true) __attribute__ ((__noreturn__));
+
+
+
+extern int atexit (void (*__func) (void)) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+extern "C++" int at_quick_exit (void (*__func) (void))
+     noexcept (true) __asm ("at_quick_exit") __attribute__ ((__nonnull__ (1)));
+# 749 "/usr/include/stdlib.h" 3 4
+extern int on_exit (void (*__func) (int __status, void *__arg), void *__arg)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+extern void exit (int __status) noexcept (true) __attribute__ ((__noreturn__));
+
+
+
+
+
+extern void quick_exit (int __status) noexcept (true) __attribute__ ((__noreturn__));
+
+
+
+
+
+extern void _Exit (int __status) noexcept (true) __attribute__ ((__noreturn__));
+
+
+
+
+extern char *getenv (const char *__name) noexcept (true) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+
+extern char *secure_getenv (const char *__name)
+     noexcept (true) __attribute__ ((__nonnull__ (1))) ;
+
+
+
+
+
+
+extern int putenv (char *__string) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+extern int setenv (const char *__name, const char *__value, int __replace)
+     noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+extern int unsetenv (const char *__name) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+
+extern int clearenv (void) noexcept (true);
+# 814 "/usr/include/stdlib.h" 3 4
+extern char *mktemp (char *__template) noexcept (true) __attribute__ ((__nonnull__ (1)));
+# 827 "/usr/include/stdlib.h" 3 4
+extern int mkstemp (char *__template) __attribute__ ((__nonnull__ (1))) ;
+# 837 "/usr/include/stdlib.h" 3 4
+extern int mkstemp64 (char *__template) __attribute__ ((__nonnull__ (1))) ;
+# 849 "/usr/include/stdlib.h" 3 4
+extern int mkstemps (char *__template, int __suffixlen) __attribute__ ((__nonnull__ (1))) ;
+# 859 "/usr/include/stdlib.h" 3 4
+extern int mkstemps64 (char *__template, int __suffixlen)
+     __attribute__ ((__nonnull__ (1))) ;
+# 870 "/usr/include/stdlib.h" 3 4
+extern char *mkdtemp (char *__template) noexcept (true) __attribute__ ((__nonnull__ (1))) ;
+# 881 "/usr/include/stdlib.h" 3 4
+extern int mkostemp (char *__template, int __flags) __attribute__ ((__nonnull__ (1))) ;
+# 891 "/usr/include/stdlib.h" 3 4
+extern int mkostemp64 (char *__template, int __flags) __attribute__ ((__nonnull__ (1))) ;
+# 901 "/usr/include/stdlib.h" 3 4
+extern int mkostemps (char *__template, int __suffixlen, int __flags)
+     __attribute__ ((__nonnull__ (1))) ;
+# 913 "/usr/include/stdlib.h" 3 4
+extern int mkostemps64 (char *__template, int __suffixlen, int __flags)
+     __attribute__ ((__nonnull__ (1))) ;
+# 923 "/usr/include/stdlib.h" 3 4
+extern int system (const char *__command) ;
+
+
+
+
+
+extern char *canonicalize_file_name (const char *__name)
+     noexcept (true) __attribute__ ((__nonnull__ (1))) __attribute__ ((__malloc__))
+     __attribute__ ((__malloc__ (__builtin_free, 1))) ;
+# 940 "/usr/include/stdlib.h" 3 4
+extern char *realpath (const char *__restrict __name,
+         char *__restrict __resolved) noexcept (true) ;
+
+
+
+
+
+
+typedef int (*__compar_fn_t) (const void *, const void *);
+
+
+typedef __compar_fn_t comparison_fn_t;
+
+
+
+typedef int (*__compar_d_fn_t) (const void *, const void *, void *);
+
+
+
+
+extern void *bsearch (const void *__key, const void *__base,
+        size_t __nmemb, size_t __size, __compar_fn_t __compar)
+     __attribute__ ((__nonnull__ (1, 2, 5))) ;
+
+
+
+
+
+
+
+extern void qsort (void *__base, size_t __nmemb, size_t __size,
+     __compar_fn_t __compar) __attribute__ ((__nonnull__ (1, 4)));
+
+extern void qsort_r (void *__base, size_t __nmemb, size_t __size,
+       __compar_d_fn_t __compar, void *__arg)
+  __attribute__ ((__nonnull__ (1, 4)));
+
+
+
+
+extern int abs (int __x) noexcept (true) __attribute__ ((__const__)) ;
+extern long int labs (long int __x) noexcept (true) __attribute__ ((__const__)) ;
+
+
+__extension__ extern long long int llabs (long long int __x)
+     noexcept (true) __attribute__ ((__const__)) ;
+
+
+
+
+
+
+extern div_t div (int __numer, int __denom)
+     noexcept (true) __attribute__ ((__const__)) ;
+extern ldiv_t ldiv (long int __numer, long int __denom)
+     noexcept (true) __attribute__ ((__const__)) ;
+
+
+__extension__ extern lldiv_t lldiv (long long int __numer,
+        long long int __denom)
+     noexcept (true) __attribute__ ((__const__)) ;
+# 1012 "/usr/include/stdlib.h" 3 4
+extern char *ecvt (double __value, int __ndigit, int *__restrict __decpt,
+     int *__restrict __sign) noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
+
+
+
+
+extern char *fcvt (double __value, int __ndigit, int *__restrict __decpt,
+     int *__restrict __sign) noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
+
+
+
+
+extern char *gcvt (double __value, int __ndigit, char *__buf)
+     noexcept (true) __attribute__ ((__nonnull__ (3))) ;
+
+
+
+
+extern char *qecvt (long double __value, int __ndigit,
+      int *__restrict __decpt, int *__restrict __sign)
+     noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
+extern char *qfcvt (long double __value, int __ndigit,
+      int *__restrict __decpt, int *__restrict __sign)
+     noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
+extern char *qgcvt (long double __value, int __ndigit, char *__buf)
+     noexcept (true) __attribute__ ((__nonnull__ (3))) ;
+
+
+
+
+extern int ecvt_r (double __value, int __ndigit, int *__restrict __decpt,
+     int *__restrict __sign, char *__restrict __buf,
+     size_t __len) noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
+extern int fcvt_r (double __value, int __ndigit, int *__restrict __decpt,
+     int *__restrict __sign, char *__restrict __buf,
+     size_t __len) noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
+
+extern int qecvt_r (long double __value, int __ndigit,
+      int *__restrict __decpt, int *__restrict __sign,
+      char *__restrict __buf, size_t __len)
+     noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
+extern int qfcvt_r (long double __value, int __ndigit,
+      int *__restrict __decpt, int *__restrict __sign,
+      char *__restrict __buf, size_t __len)
+     noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
+
+
+
+
+
+extern int mblen (const char *__s, size_t __n) noexcept (true);
+
+
+extern int mbtowc (wchar_t *__restrict __pwc,
+     const char *__restrict __s, size_t __n) noexcept (true);
+
+
+extern int wctomb (char *__s, wchar_t __wchar) noexcept (true);
+
+
+
+extern size_t mbstowcs (wchar_t *__restrict __pwcs,
+   const char *__restrict __s, size_t __n) noexcept (true)
+    __attribute__ ((__access__ (__read_only__, 2)));
+
+extern size_t wcstombs (char *__restrict __s,
+   const wchar_t *__restrict __pwcs, size_t __n)
+     noexcept (true)
+  __attribute__ ((__access__ (__write_only__, 1, 3)))
+  __attribute__ ((__access__ (__read_only__, 2)));
+
+
+
+
+
+
+extern int rpmatch (const char *__response) noexcept (true) __attribute__ ((__nonnull__ (1))) ;
+# 1099 "/usr/include/stdlib.h" 3 4
+extern int getsubopt (char **__restrict __optionp,
+        char *const *__restrict __tokens,
+        char **__restrict __valuep)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2, 3))) ;
+
+
+
+
+
+
+
+extern int posix_openpt (int __oflag) ;
+
+
+
+
+
+
+
+extern int grantpt (int __fd) noexcept (true);
+
+
+
+extern int unlockpt (int __fd) noexcept (true);
+
+
+
+
+extern char *ptsname (int __fd) noexcept (true) ;
+
+
+
+
+
+
+extern int ptsname_r (int __fd, char *__buf, size_t __buflen)
+     noexcept (true) __attribute__ ((__nonnull__ (2))) __attribute__ ((__access__ (__write_only__, 2, 3)));
+
+
+extern int getpt (void);
+
+
+
+
+
+
+extern int getloadavg (double __loadavg[], int __nelem)
+     noexcept (true) __attribute__ ((__nonnull__ (1)));
+# 1155 "/usr/include/stdlib.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/stdlib-float.h" 1 3 4
+# 1156 "/usr/include/stdlib.h" 2 3 4
+# 1167 "/usr/include/stdlib.h" 3 4
+}
+# 39 "/usr/include/c++/13/bits/std_abs.h" 2 3
+
+
+
+
+
+
+
+extern "C++"
+{
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  using ::abs;
+
+
+  inline long
+  abs(long __i) { return __builtin_labs(__i); }
+
+
+
+  inline long long
+  abs(long long __x) { return __builtin_llabs (__x); }
+# 70 "/usr/include/c++/13/bits/std_abs.h" 3
+  inline constexpr double
+  abs(double __x)
+  { return __builtin_fabs(__x); }
+
+  inline constexpr float
+  abs(float __x)
+  { return __builtin_fabsf(__x); }
+
+  inline constexpr long double
+  abs(long double __x)
+  { return __builtin_fabsl(__x); }
+
+
+
+  __extension__ inline constexpr __int128
+  abs(__int128 __x) { return __x >= 0 ? __x : -__x; }
+# 150 "/usr/include/c++/13/bits/std_abs.h" 3
+
+}
+}
+# 50 "/usr/include/c++/13/cmath" 2 3
+# 79 "/usr/include/c++/13/cmath" 3
+extern "C++"
+{
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  using ::acos;
+
+
+  inline constexpr float
+  acos(float __x)
+  { return __builtin_acosf(__x); }
+
+  inline constexpr long double
+  acos(long double __x)
+  { return __builtin_acosl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    acos(_Tp __x)
+    { return __builtin_acos(__x); }
+
+  using ::asin;
+
+
+  inline constexpr float
+  asin(float __x)
+  { return __builtin_asinf(__x); }
+
+  inline constexpr long double
+  asin(long double __x)
+  { return __builtin_asinl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    asin(_Tp __x)
+    { return __builtin_asin(__x); }
+
+  using ::atan;
+
+
+  inline constexpr float
+  atan(float __x)
+  { return __builtin_atanf(__x); }
+
+  inline constexpr long double
+  atan(long double __x)
+  { return __builtin_atanl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    atan(_Tp __x)
+    { return __builtin_atan(__x); }
+
+  using ::atan2;
+
+
+  inline constexpr float
+  atan2(float __y, float __x)
+  { return __builtin_atan2f(__y, __x); }
+
+  inline constexpr long double
+  atan2(long double __y, long double __x)
+  { return __builtin_atan2l(__y, __x); }
+
+
+  using ::ceil;
+
+
+  inline constexpr float
+  ceil(float __x)
+  { return __builtin_ceilf(__x); }
+
+  inline constexpr long double
+  ceil(long double __x)
+  { return __builtin_ceill(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    ceil(_Tp __x)
+    { return __builtin_ceil(__x); }
+
+  using ::cos;
+
+
+  inline constexpr float
+  cos(float __x)
+  { return __builtin_cosf(__x); }
+
+  inline constexpr long double
+  cos(long double __x)
+  { return __builtin_cosl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    cos(_Tp __x)
+    { return __builtin_cos(__x); }
+
+  using ::cosh;
+
+
+  inline constexpr float
+  cosh(float __x)
+  { return __builtin_coshf(__x); }
+
+  inline constexpr long double
+  cosh(long double __x)
+  { return __builtin_coshl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    cosh(_Tp __x)
+    { return __builtin_cosh(__x); }
+
+  using ::exp;
+
+
+  inline constexpr float
+  exp(float __x)
+  { return __builtin_expf(__x); }
+
+  inline constexpr long double
+  exp(long double __x)
+  { return __builtin_expl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    exp(_Tp __x)
+    { return __builtin_exp(__x); }
+
+  using ::fabs;
+
+
+  inline constexpr float
+  fabs(float __x)
+  { return __builtin_fabsf(__x); }
+
+  inline constexpr long double
+  fabs(long double __x)
+  { return __builtin_fabsl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    fabs(_Tp __x)
+    { return __builtin_fabs(__x); }
+
+  using ::floor;
+
+
+  inline constexpr float
+  floor(float __x)
+  { return __builtin_floorf(__x); }
+
+  inline constexpr long double
+  floor(long double __x)
+  { return __builtin_floorl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    floor(_Tp __x)
+    { return __builtin_floor(__x); }
+
+  using ::fmod;
+
+
+  inline constexpr float
+  fmod(float __x, float __y)
+  { return __builtin_fmodf(__x, __y); }
+
+  inline constexpr long double
+  fmod(long double __x, long double __y)
+  { return __builtin_fmodl(__x, __y); }
+
+
+  using ::frexp;
+
+
+  inline float
+  frexp(float __x, int* __exp)
+  { return __builtin_frexpf(__x, __exp); }
+
+  inline long double
+  frexp(long double __x, int* __exp)
+  { return __builtin_frexpl(__x, __exp); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    frexp(_Tp __x, int* __exp)
+    { return __builtin_frexp(__x, __exp); }
+
+  using ::ldexp;
+
+
+  inline constexpr float
+  ldexp(float __x, int __exp)
+  { return __builtin_ldexpf(__x, __exp); }
+
+  inline constexpr long double
+  ldexp(long double __x, int __exp)
+  { return __builtin_ldexpl(__x, __exp); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    ldexp(_Tp __x, int __exp)
+    { return __builtin_ldexp(__x, __exp); }
+
+  using ::log;
+
+
+  inline constexpr float
+  log(float __x)
+  { return __builtin_logf(__x); }
+
+  inline constexpr long double
+  log(long double __x)
+  { return __builtin_logl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    log(_Tp __x)
+    { return __builtin_log(__x); }
+
+  using ::log10;
+
+
+  inline constexpr float
+  log10(float __x)
+  { return __builtin_log10f(__x); }
+
+  inline constexpr long double
+  log10(long double __x)
+  { return __builtin_log10l(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    log10(_Tp __x)
+    { return __builtin_log10(__x); }
+
+  using ::modf;
+
+
+  inline float
+  modf(float __x, float* __iptr)
+  { return __builtin_modff(__x, __iptr); }
+
+  inline long double
+  modf(long double __x, long double* __iptr)
+  { return __builtin_modfl(__x, __iptr); }
+
+
+  using ::pow;
+
+
+  inline constexpr float
+  pow(float __x, float __y)
+  { return __builtin_powf(__x, __y); }
+
+  inline constexpr long double
+  pow(long double __x, long double __y)
+  { return __builtin_powl(__x, __y); }
+# 396 "/usr/include/c++/13/cmath" 3
+  using ::sin;
+
+
+  inline constexpr float
+  sin(float __x)
+  { return __builtin_sinf(__x); }
+
+  inline constexpr long double
+  sin(long double __x)
+  { return __builtin_sinl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    sin(_Tp __x)
+    { return __builtin_sin(__x); }
+
+  using ::sinh;
+
+
+  inline constexpr float
+  sinh(float __x)
+  { return __builtin_sinhf(__x); }
+
+  inline constexpr long double
+  sinh(long double __x)
+  { return __builtin_sinhl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    sinh(_Tp __x)
+    { return __builtin_sinh(__x); }
+
+  using ::sqrt;
+
+
+  inline constexpr float
+  sqrt(float __x)
+  { return __builtin_sqrtf(__x); }
+
+  inline constexpr long double
+  sqrt(long double __x)
+  { return __builtin_sqrtl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    sqrt(_Tp __x)
+    { return __builtin_sqrt(__x); }
+
+  using ::tan;
+
+
+  inline constexpr float
+  tan(float __x)
+  { return __builtin_tanf(__x); }
+
+  inline constexpr long double
+  tan(long double __x)
+  { return __builtin_tanl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    tan(_Tp __x)
+    { return __builtin_tan(__x); }
+
+  using ::tanh;
+
+
+  inline constexpr float
+  tanh(float __x)
+  { return __builtin_tanhf(__x); }
+
+  inline constexpr long double
+  tanh(long double __x)
+  { return __builtin_tanhl(__x); }
+
+
+  template<typename _Tp>
+    inline constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    double>::__type
+    tanh(_Tp __x)
+    { return __builtin_tanh(__x); }
+# 1049 "/usr/include/c++/13/cmath" 3
+  template<typename _Tp, typename _Up>
+    inline constexpr
+    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    atan2(_Tp __y, _Up __x)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return atan2(__type(__y), __type(__x));
+    }
+
+  template<typename _Tp, typename _Up>
+    inline constexpr
+    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    fmod(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return fmod(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    inline constexpr
+    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    pow(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return pow(__type(__x), __type(__y));
+    }
+# 1096 "/usr/include/c++/13/cmath" 3
+  constexpr int
+  fpclassify(float __x)
+  { return __builtin_fpclassify(0, 1, 4,
+    3, 2, __x); }
+
+  constexpr int
+  fpclassify(double __x)
+  { return __builtin_fpclassify(0, 1, 4,
+    3, 2, __x); }
+
+  constexpr int
+  fpclassify(long double __x)
+  { return __builtin_fpclassify(0, 1, 4,
+    3, 2, __x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              int>::__type
+    fpclassify(_Tp __x)
+    { return __x != 0 ? 4 : 2; }
+
+
+
+  constexpr bool
+  isfinite(float __x)
+  { return __builtin_isfinite(__x); }
+
+  constexpr bool
+  isfinite(double __x)
+  { return __builtin_isfinite(__x); }
+
+  constexpr bool
+  isfinite(long double __x)
+  { return __builtin_isfinite(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              bool>::__type
+    isfinite(_Tp)
+    { return true; }
+
+
+
+  constexpr bool
+  isinf(float __x)
+  { return __builtin_isinf(__x); }
+
+
+
+
+
+  constexpr bool
+  isinf(double __x)
+  { return __builtin_isinf(__x); }
+
+
+  constexpr bool
+  isinf(long double __x)
+  { return __builtin_isinf(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              bool>::__type
+    isinf(_Tp)
+    { return false; }
+
+
+
+  constexpr bool
+  isnan(float __x)
+  { return __builtin_isnan(__x); }
+
+
+
+
+
+  constexpr bool
+  isnan(double __x)
+  { return __builtin_isnan(__x); }
+
+
+  constexpr bool
+  isnan(long double __x)
+  { return __builtin_isnan(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              bool>::__type
+    isnan(_Tp)
+    { return false; }
+
+
+
+  constexpr bool
+  isnormal(float __x)
+  { return __builtin_isnormal(__x); }
+
+  constexpr bool
+  isnormal(double __x)
+  { return __builtin_isnormal(__x); }
+
+  constexpr bool
+  isnormal(long double __x)
+  { return __builtin_isnormal(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              bool>::__type
+    isnormal(_Tp __x)
+    { return __x != 0 ? true : false; }
+
+
+
+
+  constexpr bool
+  signbit(float __x)
+  { return __builtin_signbit(__x); }
+
+  constexpr bool
+  signbit(double __x)
+  { return __builtin_signbit(__x); }
+
+  constexpr bool
+  signbit(long double __x)
+  { return __builtin_signbit(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              bool>::__type
+    signbit(_Tp __x)
+    { return __x < 0 ? true : false; }
+
+
+
+  constexpr bool
+  isgreater(float __x, float __y)
+  { return __builtin_isgreater(__x, __y); }
+
+  constexpr bool
+  isgreater(double __x, double __y)
+  { return __builtin_isgreater(__x, __y); }
+
+  constexpr bool
+  isgreater(long double __x, long double __y)
+  { return __builtin_isgreater(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    isgreater(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_isgreater(__type(__x), __type(__y));
+    }
+
+
+
+  constexpr bool
+  isgreaterequal(float __x, float __y)
+  { return __builtin_isgreaterequal(__x, __y); }
+
+  constexpr bool
+  isgreaterequal(double __x, double __y)
+  { return __builtin_isgreaterequal(__x, __y); }
+
+  constexpr bool
+  isgreaterequal(long double __x, long double __y)
+  { return __builtin_isgreaterequal(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    isgreaterequal(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_isgreaterequal(__type(__x), __type(__y));
+    }
+
+
+
+  constexpr bool
+  isless(float __x, float __y)
+  { return __builtin_isless(__x, __y); }
+
+  constexpr bool
+  isless(double __x, double __y)
+  { return __builtin_isless(__x, __y); }
+
+  constexpr bool
+  isless(long double __x, long double __y)
+  { return __builtin_isless(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    isless(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_isless(__type(__x), __type(__y));
+    }
+
+
+
+  constexpr bool
+  islessequal(float __x, float __y)
+  { return __builtin_islessequal(__x, __y); }
+
+  constexpr bool
+  islessequal(double __x, double __y)
+  { return __builtin_islessequal(__x, __y); }
+
+  constexpr bool
+  islessequal(long double __x, long double __y)
+  { return __builtin_islessequal(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    islessequal(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_islessequal(__type(__x), __type(__y));
+    }
+
+
+
+  constexpr bool
+  islessgreater(float __x, float __y)
+  { return __builtin_islessgreater(__x, __y); }
+
+  constexpr bool
+  islessgreater(double __x, double __y)
+  { return __builtin_islessgreater(__x, __y); }
+
+  constexpr bool
+  islessgreater(long double __x, long double __y)
+  { return __builtin_islessgreater(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    islessgreater(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_islessgreater(__type(__x), __type(__y));
+    }
+
+
+
+  constexpr bool
+  isunordered(float __x, float __y)
+  { return __builtin_isunordered(__x, __y); }
+
+  constexpr bool
+  isunordered(double __x, double __y)
+  { return __builtin_isunordered(__x, __y); }
+
+  constexpr bool
+  isunordered(long double __x, long double __y)
+  { return __builtin_isunordered(__x, __y); }
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr typename
+    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
+       && __is_arithmetic<_Up>::__value), bool>::__type
+    isunordered(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return __builtin_isunordered(__type(__x), __type(__y));
+    }
+# 1881 "/usr/include/c++/13/cmath" 3
+  using ::double_t;
+  using ::float_t;
+
+
+  using ::acosh;
+  using ::acoshf;
+  using ::acoshl;
+
+  using ::asinh;
+  using ::asinhf;
+  using ::asinhl;
+
+  using ::atanh;
+  using ::atanhf;
+  using ::atanhl;
+
+  using ::cbrt;
+  using ::cbrtf;
+  using ::cbrtl;
+
+  using ::copysign;
+  using ::copysignf;
+  using ::copysignl;
+
+  using ::erf;
+  using ::erff;
+  using ::erfl;
+
+  using ::erfc;
+  using ::erfcf;
+  using ::erfcl;
+
+  using ::exp2;
+  using ::exp2f;
+  using ::exp2l;
+
+  using ::expm1;
+  using ::expm1f;
+  using ::expm1l;
+
+  using ::fdim;
+  using ::fdimf;
+  using ::fdiml;
+
+  using ::fma;
+  using ::fmaf;
+  using ::fmal;
+
+  using ::fmax;
+  using ::fmaxf;
+  using ::fmaxl;
+
+  using ::fmin;
+  using ::fminf;
+  using ::fminl;
+
+  using ::hypot;
+  using ::hypotf;
+  using ::hypotl;
+
+  using ::ilogb;
+  using ::ilogbf;
+  using ::ilogbl;
+
+  using ::lgamma;
+  using ::lgammaf;
+  using ::lgammal;
+
+
+  using ::llrint;
+  using ::llrintf;
+  using ::llrintl;
+
+  using ::llround;
+  using ::llroundf;
+  using ::llroundl;
+
+
+  using ::log1p;
+  using ::log1pf;
+  using ::log1pl;
+
+  using ::log2;
+  using ::log2f;
+  using ::log2l;
+
+  using ::logb;
+  using ::logbf;
+  using ::logbl;
+
+  using ::lrint;
+  using ::lrintf;
+  using ::lrintl;
+
+  using ::lround;
+  using ::lroundf;
+  using ::lroundl;
+
+  using ::nan;
+  using ::nanf;
+  using ::nanl;
+
+  using ::nearbyint;
+  using ::nearbyintf;
+  using ::nearbyintl;
+
+  using ::nextafter;
+  using ::nextafterf;
+  using ::nextafterl;
+
+  using ::nexttoward;
+  using ::nexttowardf;
+  using ::nexttowardl;
+
+  using ::remainder;
+  using ::remainderf;
+  using ::remainderl;
+
+  using ::remquo;
+  using ::remquof;
+  using ::remquol;
+
+  using ::rint;
+  using ::rintf;
+  using ::rintl;
+
+  using ::round;
+  using ::roundf;
+  using ::roundl;
+
+  using ::scalbln;
+  using ::scalblnf;
+  using ::scalblnl;
+
+  using ::scalbn;
+  using ::scalbnf;
+  using ::scalbnl;
+
+  using ::tgamma;
+  using ::tgammaf;
+  using ::tgammal;
+
+  using ::trunc;
+  using ::truncf;
+  using ::truncl;
+
+
+
+  constexpr float
+  acosh(float __x)
+  { return __builtin_acoshf(__x); }
+
+  constexpr long double
+  acosh(long double __x)
+  { return __builtin_acoshl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    acosh(_Tp __x)
+    { return __builtin_acosh(__x); }
+
+
+
+  constexpr float
+  asinh(float __x)
+  { return __builtin_asinhf(__x); }
+
+  constexpr long double
+  asinh(long double __x)
+  { return __builtin_asinhl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    asinh(_Tp __x)
+    { return __builtin_asinh(__x); }
+
+
+
+  constexpr float
+  atanh(float __x)
+  { return __builtin_atanhf(__x); }
+
+  constexpr long double
+  atanh(long double __x)
+  { return __builtin_atanhl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    atanh(_Tp __x)
+    { return __builtin_atanh(__x); }
+
+
+
+  constexpr float
+  cbrt(float __x)
+  { return __builtin_cbrtf(__x); }
+
+  constexpr long double
+  cbrt(long double __x)
+  { return __builtin_cbrtl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    cbrt(_Tp __x)
+    { return __builtin_cbrt(__x); }
+
+
+
+  constexpr float
+  copysign(float __x, float __y)
+  { return __builtin_copysignf(__x, __y); }
+
+  constexpr long double
+  copysign(long double __x, long double __y)
+  { return __builtin_copysignl(__x, __y); }
+
+
+
+  constexpr float
+  erf(float __x)
+  { return __builtin_erff(__x); }
+
+  constexpr long double
+  erf(long double __x)
+  { return __builtin_erfl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    erf(_Tp __x)
+    { return __builtin_erf(__x); }
+
+
+
+  constexpr float
+  erfc(float __x)
+  { return __builtin_erfcf(__x); }
+
+  constexpr long double
+  erfc(long double __x)
+  { return __builtin_erfcl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    erfc(_Tp __x)
+    { return __builtin_erfc(__x); }
+
+
+
+  constexpr float
+  exp2(float __x)
+  { return __builtin_exp2f(__x); }
+
+  constexpr long double
+  exp2(long double __x)
+  { return __builtin_exp2l(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    exp2(_Tp __x)
+    { return __builtin_exp2(__x); }
+
+
+
+  constexpr float
+  expm1(float __x)
+  { return __builtin_expm1f(__x); }
+
+  constexpr long double
+  expm1(long double __x)
+  { return __builtin_expm1l(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    expm1(_Tp __x)
+    { return __builtin_expm1(__x); }
+
+
+
+  constexpr float
+  fdim(float __x, float __y)
+  { return __builtin_fdimf(__x, __y); }
+
+  constexpr long double
+  fdim(long double __x, long double __y)
+  { return __builtin_fdiml(__x, __y); }
+
+
+
+  constexpr float
+  fma(float __x, float __y, float __z)
+  { return __builtin_fmaf(__x, __y, __z); }
+
+  constexpr long double
+  fma(long double __x, long double __y, long double __z)
+  { return __builtin_fmal(__x, __y, __z); }
+
+
+
+  constexpr float
+  fmax(float __x, float __y)
+  { return __builtin_fmaxf(__x, __y); }
+
+  constexpr long double
+  fmax(long double __x, long double __y)
+  { return __builtin_fmaxl(__x, __y); }
+
+
+
+  constexpr float
+  fmin(float __x, float __y)
+  { return __builtin_fminf(__x, __y); }
+
+  constexpr long double
+  fmin(long double __x, long double __y)
+  { return __builtin_fminl(__x, __y); }
+
+
+
+  constexpr float
+  hypot(float __x, float __y)
+  { return __builtin_hypotf(__x, __y); }
+
+  constexpr long double
+  hypot(long double __x, long double __y)
+  { return __builtin_hypotl(__x, __y); }
+
+
+
+  constexpr int
+  ilogb(float __x)
+  { return __builtin_ilogbf(__x); }
+
+  constexpr int
+  ilogb(long double __x)
+  { return __builtin_ilogbl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr
+    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                    int>::__type
+    ilogb(_Tp __x)
+    { return __builtin_ilogb(__x); }
+
+
+
+  constexpr float
+  lgamma(float __x)
+  { return __builtin_lgammaf(__x); }
+
+  constexpr long double
+  lgamma(long double __x)
+  { return __builtin_lgammal(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    lgamma(_Tp __x)
+    { return __builtin_lgamma(__x); }
+
+
+
+  constexpr long long
+  llrint(float __x)
+  { return __builtin_llrintf(__x); }
+
+  constexpr long long
+  llrint(long double __x)
+  { return __builtin_llrintl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              long long>::__type
+    llrint(_Tp __x)
+    { return __builtin_llrint(__x); }
+
+
+
+  constexpr long long
+  llround(float __x)
+  { return __builtin_llroundf(__x); }
+
+  constexpr long long
+  llround(long double __x)
+  { return __builtin_llroundl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              long long>::__type
+    llround(_Tp __x)
+    { return __builtin_llround(__x); }
+
+
+
+  constexpr float
+  log1p(float __x)
+  { return __builtin_log1pf(__x); }
+
+  constexpr long double
+  log1p(long double __x)
+  { return __builtin_log1pl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    log1p(_Tp __x)
+    { return __builtin_log1p(__x); }
+
+
+
+
+  constexpr float
+  log2(float __x)
+  { return __builtin_log2f(__x); }
+
+  constexpr long double
+  log2(long double __x)
+  { return __builtin_log2l(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    log2(_Tp __x)
+    { return __builtin_log2(__x); }
+
+
+
+  constexpr float
+  logb(float __x)
+  { return __builtin_logbf(__x); }
+
+  constexpr long double
+  logb(long double __x)
+  { return __builtin_logbl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    logb(_Tp __x)
+    { return __builtin_logb(__x); }
+
+
+
+  constexpr long
+  lrint(float __x)
+  { return __builtin_lrintf(__x); }
+
+  constexpr long
+  lrint(long double __x)
+  { return __builtin_lrintl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              long>::__type
+    lrint(_Tp __x)
+    { return __builtin_lrint(__x); }
+
+
+
+  constexpr long
+  lround(float __x)
+  { return __builtin_lroundf(__x); }
+
+  constexpr long
+  lround(long double __x)
+  { return __builtin_lroundl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              long>::__type
+    lround(_Tp __x)
+    { return __builtin_lround(__x); }
+
+
+
+  constexpr float
+  nearbyint(float __x)
+  { return __builtin_nearbyintf(__x); }
+
+  constexpr long double
+  nearbyint(long double __x)
+  { return __builtin_nearbyintl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    nearbyint(_Tp __x)
+    { return __builtin_nearbyint(__x); }
+
+
+
+  constexpr float
+  nextafter(float __x, float __y)
+  { return __builtin_nextafterf(__x, __y); }
+
+  constexpr long double
+  nextafter(long double __x, long double __y)
+  { return __builtin_nextafterl(__x, __y); }
+
+
+
+  constexpr float
+  nexttoward(float __x, long double __y)
+  { return __builtin_nexttowardf(__x, __y); }
+
+  constexpr long double
+  nexttoward(long double __x, long double __y)
+  { return __builtin_nexttowardl(__x, __y); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    nexttoward(_Tp __x, long double __y)
+    { return __builtin_nexttoward(__x, __y); }
+
+
+
+  constexpr float
+  remainder(float __x, float __y)
+  { return __builtin_remainderf(__x, __y); }
+
+  constexpr long double
+  remainder(long double __x, long double __y)
+  { return __builtin_remainderl(__x, __y); }
+
+
+
+  inline float
+  remquo(float __x, float __y, int* __pquo)
+  { return __builtin_remquof(__x, __y, __pquo); }
+
+  inline long double
+  remquo(long double __x, long double __y, int* __pquo)
+  { return __builtin_remquol(__x, __y, __pquo); }
+
+
+
+  constexpr float
+  rint(float __x)
+  { return __builtin_rintf(__x); }
+
+  constexpr long double
+  rint(long double __x)
+  { return __builtin_rintl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    rint(_Tp __x)
+    { return __builtin_rint(__x); }
+
+
+
+  constexpr float
+  round(float __x)
+  { return __builtin_roundf(__x); }
+
+  constexpr long double
+  round(long double __x)
+  { return __builtin_roundl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    round(_Tp __x)
+    { return __builtin_round(__x); }
+
+
+
+  constexpr float
+  scalbln(float __x, long __ex)
+  { return __builtin_scalblnf(__x, __ex); }
+
+  constexpr long double
+  scalbln(long double __x, long __ex)
+  { return __builtin_scalblnl(__x, __ex); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    scalbln(_Tp __x, long __ex)
+    { return __builtin_scalbln(__x, __ex); }
+
+
+
+  constexpr float
+  scalbn(float __x, int __ex)
+  { return __builtin_scalbnf(__x, __ex); }
+
+  constexpr long double
+  scalbn(long double __x, int __ex)
+  { return __builtin_scalbnl(__x, __ex); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    scalbn(_Tp __x, int __ex)
+    { return __builtin_scalbn(__x, __ex); }
+
+
+
+  constexpr float
+  tgamma(float __x)
+  { return __builtin_tgammaf(__x); }
+
+  constexpr long double
+  tgamma(long double __x)
+  { return __builtin_tgammal(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    tgamma(_Tp __x)
+    { return __builtin_tgamma(__x); }
+
+
+
+  constexpr float
+  trunc(float __x)
+  { return __builtin_truncf(__x); }
+
+  constexpr long double
+  trunc(long double __x)
+  { return __builtin_truncl(__x); }
+
+
+
+  template<typename _Tp>
+    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
+                                              double>::__type
+    trunc(_Tp __x)
+    { return __builtin_trunc(__x); }
+# 3469 "/usr/include/c++/13/cmath" 3
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    copysign(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return copysign(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    fdim(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return fdim(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    fmax(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return fmax(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    fmin(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return fmin(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    hypot(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return hypot(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    nextafter(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return nextafter(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    remainder(_Tp __x, _Up __y)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return remainder(__type(__x), __type(__y));
+    }
+
+  template<typename _Tp, typename _Up>
+    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
+    remquo(_Tp __x, _Up __y, int* __pquo)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+      return remquo(__type(__x), __type(__y), __pquo);
+    }
+
+  template<typename _Tp, typename _Up, typename _Vp>
+    constexpr typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
+    fma(_Tp __x, _Up __y, _Vp __z)
+    {
+      typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
+      return fma(__type(__x), __type(__y), __type(__z));
+    }
+# 3550 "/usr/include/c++/13/cmath" 3
+  template<typename _Tp>
+    inline _Tp
+    __hypot3(_Tp __x, _Tp __y, _Tp __z)
+    {
+      __x = std::abs(__x);
+      __y = std::abs(__y);
+      __z = std::abs(__z);
+      if (_Tp __a = __x < __y ? __y < __z ? __z : __y : __x < __z ? __z : __x)
+ return __a * std::sqrt((__x / __a) * (__x / __a)
+          + (__y / __a) * (__y / __a)
+          + (__z / __a) * (__z / __a));
+      else
+ return {};
+    }
+
+  inline float
+  hypot(float __x, float __y, float __z)
+  { return std::__hypot3<float>(__x, __y, __z); }
+
+  inline double
+  hypot(double __x, double __y, double __z)
+  { return std::__hypot3<double>(__x, __y, __z); }
+
+  inline long double
+  hypot(long double __x, long double __y, long double __z)
+  { return std::__hypot3<long double>(__x, __y, __z); }
+
+  template<typename _Tp, typename _Up, typename _Vp>
+    __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>
+    hypot(_Tp __x, _Up __y, _Vp __z)
+    {
+      using __type = __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>;
+      return std::__hypot3<__type>(__x, __y, __z);
+    }
+# 3695 "/usr/include/c++/13/cmath" 3
+
+}
+
+
+# 1 "/usr/include/c++/13/bits/specfun.h" 1 3
+# 43 "/usr/include/c++/13/bits/specfun.h" 3
+# 1 "/usr/include/c++/13/bits/stl_algobase.h" 1 3
+# 60 "/usr/include/c++/13/bits/stl_algobase.h" 3
+# 1 "/usr/include/c++/13/bits/functexcept.h" 1 3
+# 40 "/usr/include/c++/13/bits/functexcept.h" 3
+# 1 "/usr/include/c++/13/bits/exception_defines.h" 1 3
+# 41 "/usr/include/c++/13/bits/functexcept.h" 2 3
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+  void
+  __throw_bad_exception(void) __attribute__((__noreturn__));
+
+
+  void
+  __throw_bad_alloc(void) __attribute__((__noreturn__));
+
+  void
+  __throw_bad_array_new_length(void) __attribute__((__noreturn__));
+
+
+  void
+  __throw_bad_cast(void) __attribute__((__noreturn__));
+
+  void
+  __throw_bad_typeid(void) __attribute__((__noreturn__));
+
+
+  void
+  __throw_logic_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_domain_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_invalid_argument(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_length_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_out_of_range(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_out_of_range_fmt(const char*, ...) __attribute__((__noreturn__))
+    __attribute__((__format__(__gnu_printf__, 1, 2)));
+
+  void
+  __throw_runtime_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_range_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_overflow_error(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_underflow_error(const char*) __attribute__((__noreturn__));
+
+
+  void
+  __throw_ios_failure(const char*) __attribute__((__noreturn__));
+
+  void
+  __throw_ios_failure(const char*, int) __attribute__((__noreturn__));
+
+
+  void
+  __throw_system_error(int) __attribute__((__noreturn__));
+
+
+  void
+  __throw_future_error(int) __attribute__((__noreturn__));
+
+
+  void
+  __throw_bad_function_call() __attribute__((__noreturn__));
+# 140 "/usr/include/c++/13/bits/functexcept.h" 3
+
+}
+# 61 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+
+
+# 1 "/usr/include/c++/13/ext/numeric_traits.h" 1 3
+# 32 "/usr/include/c++/13/ext/numeric_traits.h" 3
+       
+# 33 "/usr/include/c++/13/ext/numeric_traits.h" 3
+
+
+
+
+namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
+{
+
+# 50 "/usr/include/c++/13/ext/numeric_traits.h" 3
+  template<typename _Tp>
+    struct __is_integer_nonstrict
+    : public std::__is_integer<_Tp>
+    {
+      using std::__is_integer<_Tp>::__value;
+
+
+      enum { __width = __value ? sizeof(_Tp) * 8 : 0 };
+    };
+
+  template<typename _Value>
+    struct __numeric_traits_integer
+    {
+
+      static_assert(__is_integer_nonstrict<_Value>::__value,
+      "invalid specialization");
+
+
+
+
+      static const bool __is_signed = (_Value)(-1) < 0;
+      static const int __digits
+ = __is_integer_nonstrict<_Value>::__width - __is_signed;
+
+
+      static const _Value __max = __is_signed
+ ? (((((_Value)1 << (__digits - 1)) - 1) << 1) + 1)
+ : ~(_Value)0;
+      static const _Value __min = __is_signed ? -__max - 1 : (_Value)0;
+    };
+
+  template<typename _Value>
+    const _Value __numeric_traits_integer<_Value>::__min;
+
+  template<typename _Value>
+    const _Value __numeric_traits_integer<_Value>::__max;
+
+  template<typename _Value>
+    const bool __numeric_traits_integer<_Value>::__is_signed;
+
+  template<typename _Value>
+    const int __numeric_traits_integer<_Value>::__digits;
+# 137 "/usr/include/c++/13/ext/numeric_traits.h" 3
+  template<typename _Tp>
+    using __int_traits = __numeric_traits_integer<_Tp>;
+# 157 "/usr/include/c++/13/ext/numeric_traits.h" 3
+  template<typename _Value>
+    struct __numeric_traits_floating
+    {
+
+      static const int __max_digits10 = (2 + (std::__are_same<_Value, float>::__value ? 24 : std::__are_same<_Value, double>::__value ? 53 : 113) * 643L / 2136);
+
+
+      static const bool __is_signed = true;
+      static const int __digits10 = (std::__are_same<_Value, float>::__value ? 6 : std::__are_same<_Value, double>::__value ? 15 : 33);
+      static const int __max_exponent10 = (std::__are_same<_Value, float>::__value ? 38 : std::__are_same<_Value, double>::__value ? 308 : 4932);
+    };
+
+  template<typename _Value>
+    const int __numeric_traits_floating<_Value>::__max_digits10;
+
+  template<typename _Value>
+    const bool __numeric_traits_floating<_Value>::__is_signed;
+
+  template<typename _Value>
+    const int __numeric_traits_floating<_Value>::__digits10;
+
+  template<typename _Value>
+    const int __numeric_traits_floating<_Value>::__max_exponent10;
+
+
+
+
+
+
+  template<typename _Value>
+    struct __numeric_traits
+    : public __numeric_traits_integer<_Value>
+    { };
+
+  template<>
+    struct __numeric_traits<float>
+    : public __numeric_traits_floating<float>
+    { };
+
+  template<>
+    struct __numeric_traits<double>
+    : public __numeric_traits_floating<double>
+    { };
+
+  template<>
+    struct __numeric_traits<long double>
+    : public __numeric_traits_floating<long double>
+    { };
+# 238 "/usr/include/c++/13/ext/numeric_traits.h" 3
+
+}
+# 64 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+# 1 "/usr/include/c++/13/bits/stl_pair.h" 1 3
+# 60 "/usr/include/c++/13/bits/stl_pair.h" 3
+# 1 "/usr/include/c++/13/type_traits" 1 3
+# 32 "/usr/include/c++/13/type_traits" 3
+       
+# 33 "/usr/include/c++/13/type_traits" 3
+
+
+
+
+
+
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  template<typename _Tp>
+    class reference_wrapper;
+# 61 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp, _Tp __v>
+    struct integral_constant
+    {
+      static constexpr _Tp value = __v;
+      typedef _Tp value_type;
+      typedef integral_constant<_Tp, __v> type;
+      constexpr operator value_type() const noexcept { return value; }
+
+
+
+
+      constexpr value_type operator()() const noexcept { return value; }
+
+    };
+
+
+
+
+
+
+
+  using true_type = integral_constant<bool, true>;
+
+
+  using false_type = integral_constant<bool, false>;
+
+
+
+  template<bool __v>
+    using __bool_constant = integral_constant<bool, __v>;
+
+
+
+
+
+
+  template<bool __v>
+    using bool_constant = integral_constant<bool, __v>;
+
+
+
+
+
+
+  template<bool, typename _Tp = void>
+    struct enable_if
+    { };
+
+
+  template<typename _Tp>
+    struct enable_if<true, _Tp>
+    { typedef _Tp type; };
+
+
+  template<bool _Cond, typename _Tp = void>
+    using __enable_if_t = typename enable_if<_Cond, _Tp>::type;
+
+  template<bool>
+    struct __conditional
+    {
+      template<typename _Tp, typename>
+ using type = _Tp;
+    };
+
+  template<>
+    struct __conditional<false>
+    {
+      template<typename, typename _Up>
+ using type = _Up;
+    };
+
+
+  template<bool _Cond, typename _If, typename _Else>
+    using __conditional_t
+      = typename __conditional<_Cond>::template type<_If, _Else>;
+
+
+  template <typename _Type>
+    struct __type_identity
+    { using type = _Type; };
+
+  template<typename _Tp>
+    using __type_identity_t = typename __type_identity<_Tp>::type;
+
+  namespace __detail
+  {
+
+    template<typename _Tp, typename...>
+      using __first_t = _Tp;
+
+
+    template<typename... _Bn>
+      auto __or_fn(int) -> __first_t<false_type,
+         __enable_if_t<!bool(_Bn::value)>...>;
+
+    template<typename... _Bn>
+      auto __or_fn(...) -> true_type;
+
+    template<typename... _Bn>
+      auto __and_fn(int) -> __first_t<true_type,
+          __enable_if_t<bool(_Bn::value)>...>;
+
+    template<typename... _Bn>
+      auto __and_fn(...) -> false_type;
+  }
+
+
+
+
+  template<typename... _Bn>
+    struct __or_
+    : decltype(__detail::__or_fn<_Bn...>(0))
+    { };
+
+  template<typename... _Bn>
+    struct __and_
+    : decltype(__detail::__and_fn<_Bn...>(0))
+    { };
+
+  template<typename _Pp>
+    struct __not_
+    : __bool_constant<!bool(_Pp::value)>
+    { };
+
+
+
+
+
+  template<typename... _Bn>
+    inline constexpr bool __or_v = __or_<_Bn...>::value;
+  template<typename... _Bn>
+    inline constexpr bool __and_v = __and_<_Bn...>::value;
+
+  namespace __detail
+  {
+    template<typename , typename _B1, typename... _Bn>
+      struct __disjunction_impl
+      { using type = _B1; };
+
+    template<typename _B1, typename _B2, typename... _Bn>
+      struct __disjunction_impl<__enable_if_t<!bool(_B1::value)>, _B1, _B2, _Bn...>
+      { using type = typename __disjunction_impl<void, _B2, _Bn...>::type; };
+
+    template<typename , typename _B1, typename... _Bn>
+      struct __conjunction_impl
+      { using type = _B1; };
+
+    template<typename _B1, typename _B2, typename... _Bn>
+      struct __conjunction_impl<__enable_if_t<bool(_B1::value)>, _B1, _B2, _Bn...>
+      { using type = typename __conjunction_impl<void, _B2, _Bn...>::type; };
+  }
+
+
+
+
+  template<typename... _Bn>
+    struct conjunction
+    : __detail::__conjunction_impl<void, _Bn...>::type
+    { };
+
+  template<>
+    struct conjunction<>
+    : true_type
+    { };
+
+  template<typename... _Bn>
+    struct disjunction
+    : __detail::__disjunction_impl<void, _Bn...>::type
+    { };
+
+  template<>
+    struct disjunction<>
+    : false_type
+    { };
+
+  template<typename _Pp>
+    struct negation
+    : __not_<_Pp>::type
+    { };
+
+
+
+
+  template<typename... _Bn>
+    inline constexpr bool conjunction_v = conjunction<_Bn...>::value;
+
+  template<typename... _Bn>
+    inline constexpr bool disjunction_v = disjunction<_Bn...>::value;
+
+  template<typename _Pp>
+    inline constexpr bool negation_v = negation<_Pp>::value;
+
+
+
+
+
+  template<typename>
+    struct is_reference;
+  template<typename>
+    struct is_function;
+  template<typename>
+    struct is_void;
+  template<typename>
+    struct remove_cv;
+  template<typename>
+    struct is_const;
+
+
+  template<typename>
+    struct __is_array_unknown_bounds;
+
+
+
+
+  template <typename _Tp, size_t = sizeof(_Tp)>
+    constexpr true_type __is_complete_or_unbounded(__type_identity<_Tp>)
+    { return {}; }
+
+  template <typename _TypeIdentity,
+      typename _NestedType = typename _TypeIdentity::type>
+    constexpr typename __or_<
+      is_reference<_NestedType>,
+      is_function<_NestedType>,
+      is_void<_NestedType>,
+      __is_array_unknown_bounds<_NestedType>
+    >::type __is_complete_or_unbounded(_TypeIdentity)
+    { return {}; }
+
+
+  template<typename _Tp>
+    using __remove_cv_t = typename remove_cv<_Tp>::type;
+
+
+
+
+
+  template<typename _Tp>
+    struct is_void
+    : public false_type { };
+
+  template<>
+    struct is_void<void>
+    : public true_type { };
+
+  template<>
+    struct is_void<const void>
+    : public true_type { };
+
+  template<>
+    struct is_void<volatile void>
+    : public true_type { };
+
+  template<>
+    struct is_void<const volatile void>
+    : public true_type { };
+
+
+  template<typename>
+    struct __is_integral_helper
+    : public false_type { };
+
+  template<>
+    struct __is_integral_helper<bool>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<char>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<signed char>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<unsigned char>
+    : public true_type { };
+
+
+
+
+  template<>
+    struct __is_integral_helper<wchar_t>
+    : public true_type { };
+
+
+
+
+
+
+
+  template<>
+    struct __is_integral_helper<char16_t>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<char32_t>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<short>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<unsigned short>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<int>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<unsigned int>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<long>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<unsigned long>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<long long>
+    : public true_type { };
+
+  template<>
+    struct __is_integral_helper<unsigned long long>
+    : public true_type { };
+
+
+
+
+  __extension__
+  template<>
+    struct __is_integral_helper<__int128>
+    : public true_type { };
+
+  __extension__
+  template<>
+    struct __is_integral_helper<unsigned __int128>
+    : public true_type { };
+# 440 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct is_integral
+    : public __is_integral_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+
+  template<typename>
+    struct __is_floating_point_helper
+    : public false_type { };
+
+  template<>
+    struct __is_floating_point_helper<float>
+    : public true_type { };
+
+  template<>
+    struct __is_floating_point_helper<double>
+    : public true_type { };
+
+  template<>
+    struct __is_floating_point_helper<long double>
+    : public true_type { };
+# 500 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct is_floating_point
+    : public __is_floating_point_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+
+  template<typename>
+    struct is_array
+    : public false_type { };
+
+  template<typename _Tp, std::size_t _Size>
+    struct is_array<_Tp[_Size]>
+    : public true_type { };
+
+  template<typename _Tp>
+    struct is_array<_Tp[]>
+    : public true_type { };
+
+  template<typename>
+    struct __is_pointer_helper
+    : public false_type { };
+
+  template<typename _Tp>
+    struct __is_pointer_helper<_Tp*>
+    : public true_type { };
+
+
+  template<typename _Tp>
+    struct is_pointer
+    : public __is_pointer_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+
+  template<typename>
+    struct is_lvalue_reference
+    : public false_type { };
+
+  template<typename _Tp>
+    struct is_lvalue_reference<_Tp&>
+    : public true_type { };
+
+
+  template<typename>
+    struct is_rvalue_reference
+    : public false_type { };
+
+  template<typename _Tp>
+    struct is_rvalue_reference<_Tp&&>
+    : public true_type { };
+
+  template<typename>
+    struct __is_member_object_pointer_helper
+    : public false_type { };
+
+  template<typename _Tp, typename _Cp>
+    struct __is_member_object_pointer_helper<_Tp _Cp::*>
+    : public __not_<is_function<_Tp>>::type { };
+
+
+  template<typename _Tp>
+    struct is_member_object_pointer
+    : public __is_member_object_pointer_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+  template<typename>
+    struct __is_member_function_pointer_helper
+    : public false_type { };
+
+  template<typename _Tp, typename _Cp>
+    struct __is_member_function_pointer_helper<_Tp _Cp::*>
+    : public is_function<_Tp>::type { };
+
+
+  template<typename _Tp>
+    struct is_member_function_pointer
+    : public __is_member_function_pointer_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_enum
+    : public integral_constant<bool, __is_enum(_Tp)>
+    { };
+
+
+  template<typename _Tp>
+    struct is_union
+    : public integral_constant<bool, __is_union(_Tp)>
+    { };
+
+
+  template<typename _Tp>
+    struct is_class
+    : public integral_constant<bool, __is_class(_Tp)>
+    { };
+
+
+  template<typename _Tp>
+    struct is_function
+    : public __bool_constant<!is_const<const _Tp>::value> { };
+
+  template<typename _Tp>
+    struct is_function<_Tp&>
+    : public false_type { };
+
+  template<typename _Tp>
+    struct is_function<_Tp&&>
+    : public false_type { };
+
+
+
+
+  template<typename _Tp>
+    struct is_null_pointer
+    : public false_type { };
+
+  template<>
+    struct is_null_pointer<std::nullptr_t>
+    : public true_type { };
+
+  template<>
+    struct is_null_pointer<const std::nullptr_t>
+    : public true_type { };
+
+  template<>
+    struct is_null_pointer<volatile std::nullptr_t>
+    : public true_type { };
+
+  template<>
+    struct is_null_pointer<const volatile std::nullptr_t>
+    : public true_type { };
+
+
+
+  template<typename _Tp>
+    struct __is_nullptr_t
+    : public is_null_pointer<_Tp>
+    { } __attribute__ ((__deprecated__ ("use '" "std::is_null_pointer" "' instead")));
+
+
+
+
+  template<typename _Tp>
+    struct is_reference
+    : public false_type
+    { };
+
+  template<typename _Tp>
+    struct is_reference<_Tp&>
+    : public true_type
+    { };
+
+  template<typename _Tp>
+    struct is_reference<_Tp&&>
+    : public true_type
+    { };
+
+
+  template<typename _Tp>
+    struct is_arithmetic
+    : public __or_<is_integral<_Tp>, is_floating_point<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_fundamental
+    : public __or_<is_arithmetic<_Tp>, is_void<_Tp>,
+     is_null_pointer<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_object
+    : public __not_<__or_<is_function<_Tp>, is_reference<_Tp>,
+                          is_void<_Tp>>>::type
+    { };
+
+  template<typename>
+    struct is_member_pointer;
+
+
+  template<typename _Tp>
+    struct is_scalar
+    : public __or_<is_arithmetic<_Tp>, is_enum<_Tp>, is_pointer<_Tp>,
+                   is_member_pointer<_Tp>, is_null_pointer<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_compound
+    : public __not_<is_fundamental<_Tp>>::type { };
+
+
+  template<typename _Tp>
+    struct __is_member_pointer_helper
+    : public false_type { };
+
+  template<typename _Tp, typename _Cp>
+    struct __is_member_pointer_helper<_Tp _Cp::*>
+    : public true_type { };
+
+
+
+  template<typename _Tp>
+    struct is_member_pointer
+    : public __is_member_pointer_helper<__remove_cv_t<_Tp>>::type
+    { };
+
+  template<typename, typename>
+    struct is_same;
+
+
+  template<typename _Tp, typename... _Types>
+    using __is_one_of = __or_<is_same<_Tp, _Types>...>;
+
+
+  __extension__
+  template<typename _Tp>
+    using __is_signed_integer = __is_one_of<__remove_cv_t<_Tp>,
+   signed char, signed short, signed int, signed long,
+   signed long long
+
+   , signed __int128
+# 733 "/usr/include/c++/13/type_traits" 3
+   >;
+
+
+  __extension__
+  template<typename _Tp>
+    using __is_unsigned_integer = __is_one_of<__remove_cv_t<_Tp>,
+   unsigned char, unsigned short, unsigned int, unsigned long,
+   unsigned long long
+
+   , unsigned __int128
+# 753 "/usr/include/c++/13/type_traits" 3
+   >;
+
+
+  template<typename _Tp>
+    using __is_standard_integer
+      = __or_<__is_signed_integer<_Tp>, __is_unsigned_integer<_Tp>>;
+
+
+  template<typename...> using __void_t = void;
+
+
+
+
+
+  template<typename>
+    struct is_const
+    : public false_type { };
+
+  template<typename _Tp>
+    struct is_const<_Tp const>
+    : public true_type { };
+
+
+  template<typename>
+    struct is_volatile
+    : public false_type { };
+
+  template<typename _Tp>
+    struct is_volatile<_Tp volatile>
+    : public true_type { };
+
+
+  template<typename _Tp>
+    struct is_trivial
+    : public integral_constant<bool, __is_trivial(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_copyable
+    : public integral_constant<bool, __is_trivially_copyable(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_standard_layout
+    : public integral_constant<bool, __is_standard_layout(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+
+
+
+  template<typename _Tp>
+    struct
+   
+    is_pod
+    : public integral_constant<bool, __is_pod(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+
+
+  template<typename _Tp>
+    struct
+    [[__deprecated__]]
+    is_literal_type
+    : public integral_constant<bool, __is_literal_type(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_empty
+    : public integral_constant<bool, __is_empty(_Tp)>
+    { };
+
+
+  template<typename _Tp>
+    struct is_polymorphic
+    : public integral_constant<bool, __is_polymorphic(_Tp)>
+    { };
+
+
+
+
+
+  template<typename _Tp>
+    struct is_final
+    : public integral_constant<bool, __is_final(_Tp)>
+    { };
+
+
+
+  template<typename _Tp>
+    struct is_abstract
+    : public integral_constant<bool, __is_abstract(_Tp)>
+    { };
+
+
+  template<typename _Tp,
+    bool = is_arithmetic<_Tp>::value>
+    struct __is_signed_helper
+    : public false_type { };
+
+  template<typename _Tp>
+    struct __is_signed_helper<_Tp, true>
+    : public integral_constant<bool, _Tp(-1) < _Tp(0)>
+    { };
+
+
+
+  template<typename _Tp>
+    struct is_signed
+    : public __is_signed_helper<_Tp>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_unsigned
+    : public __and_<is_arithmetic<_Tp>, __not_<is_signed<_Tp>>>::type
+    { };
+
+
+  template<typename _Tp, typename _Up = _Tp&&>
+    _Up
+    __declval(int);
+
+  template<typename _Tp>
+    _Tp
+    __declval(long);
+
+
+  template<typename _Tp>
+    auto declval() noexcept -> decltype(__declval<_Tp>(0));
+
+  template<typename>
+    struct remove_all_extents;
+
+
+  template<typename _Tp>
+    struct __is_array_known_bounds
+    : public false_type
+    { };
+
+  template<typename _Tp, size_t _Size>
+    struct __is_array_known_bounds<_Tp[_Size]>
+    : public true_type
+    { };
+
+  template<typename _Tp>
+    struct __is_array_unknown_bounds
+    : public false_type
+    { };
+
+  template<typename _Tp>
+    struct __is_array_unknown_bounds<_Tp[]>
+    : public true_type
+    { };
+# 936 "/usr/include/c++/13/type_traits" 3
+  struct __do_is_destructible_impl
+  {
+    template<typename _Tp, typename = decltype(declval<_Tp&>().~_Tp())>
+      static true_type __test(int);
+
+    template<typename>
+      static false_type __test(...);
+  };
+
+  template<typename _Tp>
+    struct __is_destructible_impl
+    : public __do_is_destructible_impl
+    {
+      typedef decltype(__test<_Tp>(0)) type;
+    };
+
+  template<typename _Tp,
+           bool = __or_<is_void<_Tp>,
+                        __is_array_unknown_bounds<_Tp>,
+                        is_function<_Tp>>::value,
+           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
+    struct __is_destructible_safe;
+
+  template<typename _Tp>
+    struct __is_destructible_safe<_Tp, false, false>
+    : public __is_destructible_impl<typename
+               remove_all_extents<_Tp>::type>::type
+    { };
+
+  template<typename _Tp>
+    struct __is_destructible_safe<_Tp, true, false>
+    : public false_type { };
+
+  template<typename _Tp>
+    struct __is_destructible_safe<_Tp, false, true>
+    : public true_type { };
+
+
+
+  template<typename _Tp>
+    struct is_destructible
+    : public __is_destructible_safe<_Tp>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+
+
+
+
+  struct __do_is_nt_destructible_impl
+  {
+    template<typename _Tp>
+      static __bool_constant<noexcept(declval<_Tp&>().~_Tp())>
+      __test(int);
+
+    template<typename>
+      static false_type __test(...);
+  };
+
+  template<typename _Tp>
+    struct __is_nt_destructible_impl
+    : public __do_is_nt_destructible_impl
+    {
+      typedef decltype(__test<_Tp>(0)) type;
+    };
+
+  template<typename _Tp,
+           bool = __or_<is_void<_Tp>,
+                        __is_array_unknown_bounds<_Tp>,
+                        is_function<_Tp>>::value,
+           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
+    struct __is_nt_destructible_safe;
+
+  template<typename _Tp>
+    struct __is_nt_destructible_safe<_Tp, false, false>
+    : public __is_nt_destructible_impl<typename
+               remove_all_extents<_Tp>::type>::type
+    { };
+
+  template<typename _Tp>
+    struct __is_nt_destructible_safe<_Tp, true, false>
+    : public false_type { };
+
+  template<typename _Tp>
+    struct __is_nt_destructible_safe<_Tp, false, true>
+    : public true_type { };
+
+
+
+  template<typename _Tp>
+    struct is_nothrow_destructible
+    : public __is_nt_destructible_safe<_Tp>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename... _Args>
+    using __is_constructible_impl
+      = __bool_constant<__is_constructible(_Tp, _Args...)>;
+
+
+
+  template<typename _Tp, typename... _Args>
+    struct is_constructible
+      : public __is_constructible_impl<_Tp, _Args...>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_default_constructible
+    : public __is_constructible_impl<_Tp>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename = void>
+    struct __add_lvalue_reference_helper
+    { using type = _Tp; };
+
+  template<typename _Tp>
+    struct __add_lvalue_reference_helper<_Tp, __void_t<_Tp&>>
+    { using type = _Tp&; };
+
+  template<typename _Tp>
+    using __add_lval_ref_t = typename __add_lvalue_reference_helper<_Tp>::type;
+
+
+
+  template<typename _Tp>
+    struct is_copy_constructible
+    : public __is_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename = void>
+    struct __add_rvalue_reference_helper
+    { using type = _Tp; };
+
+  template<typename _Tp>
+    struct __add_rvalue_reference_helper<_Tp, __void_t<_Tp&&>>
+    { using type = _Tp&&; };
+
+  template<typename _Tp>
+    using __add_rval_ref_t = typename __add_rvalue_reference_helper<_Tp>::type;
+
+
+
+  template<typename _Tp>
+    struct is_move_constructible
+    : public __is_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename... _Args>
+    using __is_nothrow_constructible_impl
+      = __bool_constant<__is_nothrow_constructible(_Tp, _Args...)>;
+
+
+
+  template<typename _Tp, typename... _Args>
+    struct is_nothrow_constructible
+    : public __is_nothrow_constructible_impl<_Tp, _Args...>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_default_constructible
+    : public __is_nothrow_constructible_impl<_Tp>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_copy_constructible
+    : public __is_nothrow_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_move_constructible
+    : public __is_nothrow_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename _Up>
+    using __is_assignable_impl = __bool_constant<__is_assignable(_Tp, _Up)>;
+
+
+
+  template<typename _Tp, typename _Up>
+    struct is_assignable
+    : public __is_assignable_impl<_Tp, _Up>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_copy_assignable
+    : public __is_assignable_impl<__add_lval_ref_t<_Tp>,
+      __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_move_assignable
+    : public __is_assignable_impl<__add_lval_ref_t<_Tp>, __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename _Up>
+    using __is_nothrow_assignable_impl
+      = __bool_constant<__is_nothrow_assignable(_Tp, _Up)>;
+
+
+
+  template<typename _Tp, typename _Up>
+    struct is_nothrow_assignable
+    : public __is_nothrow_assignable_impl<_Tp, _Up>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_copy_assignable
+    : public __is_nothrow_assignable_impl<__add_lval_ref_t<_Tp>,
+       __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_move_assignable
+    : public __is_nothrow_assignable_impl<__add_lval_ref_t<_Tp>,
+       __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename... _Args>
+    using __is_trivially_constructible_impl
+      = __bool_constant<__is_trivially_constructible(_Tp, _Args...)>;
+
+
+
+  template<typename _Tp, typename... _Args>
+    struct is_trivially_constructible
+    : public __is_trivially_constructible_impl<_Tp, _Args...>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_default_constructible
+    : public __is_trivially_constructible_impl<_Tp>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+  struct __do_is_implicitly_default_constructible_impl
+  {
+    template <typename _Tp>
+    static void __helper(const _Tp&);
+
+    template <typename _Tp>
+    static true_type __test(const _Tp&,
+                            decltype(__helper<const _Tp&>({}))* = 0);
+
+    static false_type __test(...);
+  };
+
+  template<typename _Tp>
+    struct __is_implicitly_default_constructible_impl
+    : public __do_is_implicitly_default_constructible_impl
+    {
+      typedef decltype(__test(declval<_Tp>())) type;
+    };
+
+  template<typename _Tp>
+    struct __is_implicitly_default_constructible_safe
+    : public __is_implicitly_default_constructible_impl<_Tp>::type
+    { };
+
+  template <typename _Tp>
+    struct __is_implicitly_default_constructible
+    : public __and_<__is_constructible_impl<_Tp>,
+      __is_implicitly_default_constructible_safe<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+    struct is_trivially_copy_constructible
+    : public __is_trivially_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_move_constructible
+    : public __is_trivially_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename _Up>
+    using __is_trivially_assignable_impl
+      = __bool_constant<__is_trivially_assignable(_Tp, _Up)>;
+
+
+
+  template<typename _Tp, typename _Up>
+    struct is_trivially_assignable
+    : public __is_trivially_assignable_impl<_Tp, _Up>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_copy_assignable
+    : public __is_trivially_assignable_impl<__add_lval_ref_t<_Tp>,
+         __add_lval_ref_t<const _Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_move_assignable
+    : public __is_trivially_assignable_impl<__add_lval_ref_t<_Tp>,
+         __add_rval_ref_t<_Tp>>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_trivially_destructible
+    : public __and_<__is_destructible_safe<_Tp>,
+      __bool_constant<__has_trivial_destructor(_Tp)>>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+  template<typename _Tp>
+    struct has_virtual_destructor
+    : public integral_constant<bool, __has_virtual_destructor(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+
+
+  template<typename _Tp>
+    struct alignment_of
+    : public integral_constant<std::size_t, alignof(_Tp)>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename>
+    struct rank
+    : public integral_constant<std::size_t, 0> { };
+
+  template<typename _Tp, std::size_t _Size>
+    struct rank<_Tp[_Size]>
+    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
+
+  template<typename _Tp>
+    struct rank<_Tp[]>
+    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
+
+
+  template<typename, unsigned _Uint = 0>
+    struct extent
+    : public integral_constant<size_t, 0> { };
+
+  template<typename _Tp, size_t _Size>
+    struct extent<_Tp[_Size], 0>
+    : public integral_constant<size_t, _Size> { };
+
+  template<typename _Tp, unsigned _Uint, size_t _Size>
+    struct extent<_Tp[_Size], _Uint>
+    : public extent<_Tp, _Uint - 1>::type { };
+
+  template<typename _Tp>
+    struct extent<_Tp[], 0>
+    : public integral_constant<size_t, 0> { };
+
+  template<typename _Tp, unsigned _Uint>
+    struct extent<_Tp[], _Uint>
+    : public extent<_Tp, _Uint - 1>::type { };
+
+
+
+
+
+  template<typename _Tp, typename _Up>
+    struct is_same
+
+    : public integral_constant<bool, __is_same(_Tp, _Up)>
+
+
+
+    { };
+# 1409 "/usr/include/c++/13/type_traits" 3
+  template<typename _Base, typename _Derived>
+    struct is_base_of
+    : public integral_constant<bool, __is_base_of(_Base, _Derived)>
+    { };
+
+
+  template<typename _From, typename _To>
+    struct is_convertible
+    : public __bool_constant<__is_convertible(_From, _To)>
+    { };
+# 1458 "/usr/include/c++/13/type_traits" 3
+  template<typename _ToElementType, typename _FromElementType>
+    using __is_array_convertible
+      = is_convertible<_FromElementType(*)[], _ToElementType(*)[]>;
+# 1522 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct remove_const
+    { typedef _Tp type; };
+
+  template<typename _Tp>
+    struct remove_const<_Tp const>
+    { typedef _Tp type; };
+
+
+  template<typename _Tp>
+    struct remove_volatile
+    { typedef _Tp type; };
+
+  template<typename _Tp>
+    struct remove_volatile<_Tp volatile>
+    { typedef _Tp type; };
+
+
+
+  template<typename _Tp>
+    struct remove_cv
+    { using type = __remove_cv(_Tp); };
+# 1563 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct add_const
+    { using type = _Tp const; };
+
+
+  template<typename _Tp>
+    struct add_volatile
+    { using type = _Tp volatile; };
+
+
+  template<typename _Tp>
+    struct add_cv
+    { using type = _Tp const volatile; };
+
+
+
+
+
+
+  template<typename _Tp>
+    using remove_const_t = typename remove_const<_Tp>::type;
+
+
+  template<typename _Tp>
+    using remove_volatile_t = typename remove_volatile<_Tp>::type;
+
+
+  template<typename _Tp>
+    using remove_cv_t = typename remove_cv<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_const_t = typename add_const<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_volatile_t = typename add_volatile<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_cv_t = typename add_cv<_Tp>::type;
+
+
+
+
+
+
+  template<typename _Tp>
+    struct remove_reference
+    { using type = __remove_reference(_Tp); };
+# 1628 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct add_lvalue_reference
+    { using type = __add_lval_ref_t<_Tp>; };
+
+
+  template<typename _Tp>
+    struct add_rvalue_reference
+    { using type = __add_rval_ref_t<_Tp>; };
+
+
+
+  template<typename _Tp>
+    using remove_reference_t = typename remove_reference<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_lvalue_reference_t = typename add_lvalue_reference<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_rvalue_reference_t = typename add_rvalue_reference<_Tp>::type;
+
+
+
+
+
+
+
+  template<typename _Unqualified, bool _IsConst, bool _IsVol>
+    struct __cv_selector;
+
+  template<typename _Unqualified>
+    struct __cv_selector<_Unqualified, false, false>
+    { typedef _Unqualified __type; };
+
+  template<typename _Unqualified>
+    struct __cv_selector<_Unqualified, false, true>
+    { typedef volatile _Unqualified __type; };
+
+  template<typename _Unqualified>
+    struct __cv_selector<_Unqualified, true, false>
+    { typedef const _Unqualified __type; };
+
+  template<typename _Unqualified>
+    struct __cv_selector<_Unqualified, true, true>
+    { typedef const volatile _Unqualified __type; };
+
+  template<typename _Qualified, typename _Unqualified,
+    bool _IsConst = is_const<_Qualified>::value,
+    bool _IsVol = is_volatile<_Qualified>::value>
+    class __match_cv_qualifiers
+    {
+      typedef __cv_selector<_Unqualified, _IsConst, _IsVol> __match;
+
+    public:
+      typedef typename __match::__type __type;
+    };
+
+
+  template<typename _Tp>
+    struct __make_unsigned
+    { typedef _Tp __type; };
+
+  template<>
+    struct __make_unsigned<char>
+    { typedef unsigned char __type; };
+
+  template<>
+    struct __make_unsigned<signed char>
+    { typedef unsigned char __type; };
+
+  template<>
+    struct __make_unsigned<short>
+    { typedef unsigned short __type; };
+
+  template<>
+    struct __make_unsigned<int>
+    { typedef unsigned int __type; };
+
+  template<>
+    struct __make_unsigned<long>
+    { typedef unsigned long __type; };
+
+  template<>
+    struct __make_unsigned<long long>
+    { typedef unsigned long long __type; };
+
+
+  __extension__
+  template<>
+    struct __make_unsigned<__int128>
+    { typedef unsigned __int128 __type; };
+# 1741 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp,
+    bool _IsInt = is_integral<_Tp>::value,
+    bool _IsEnum = is_enum<_Tp>::value>
+    class __make_unsigned_selector;
+
+  template<typename _Tp>
+    class __make_unsigned_selector<_Tp, true, false>
+    {
+      using __unsigned_type
+ = typename __make_unsigned<__remove_cv_t<_Tp>>::__type;
+
+    public:
+      using __type
+ = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
+    };
+
+  class __make_unsigned_selector_base
+  {
+  protected:
+    template<typename...> struct _List { };
+
+    template<typename _Tp, typename... _Up>
+      struct _List<_Tp, _Up...> : _List<_Up...>
+      { static constexpr size_t __size = sizeof(_Tp); };
+
+    template<size_t _Sz, typename _Tp, bool = (_Sz <= _Tp::__size)>
+      struct __select;
+
+    template<size_t _Sz, typename _Uint, typename... _UInts>
+      struct __select<_Sz, _List<_Uint, _UInts...>, true>
+      { using __type = _Uint; };
+
+    template<size_t _Sz, typename _Uint, typename... _UInts>
+      struct __select<_Sz, _List<_Uint, _UInts...>, false>
+      : __select<_Sz, _List<_UInts...>>
+      { };
+  };
+
+
+  template<typename _Tp>
+    class __make_unsigned_selector<_Tp, false, true>
+    : __make_unsigned_selector_base
+    {
+
+      using _UInts = _List<unsigned char, unsigned short, unsigned int,
+      unsigned long, unsigned long long>;
+
+      using __unsigned_type = typename __select<sizeof(_Tp), _UInts>::__type;
+
+    public:
+      using __type
+ = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
+    };
+
+
+
+
+
+  template<>
+    struct __make_unsigned<wchar_t>
+    {
+      using __type
+ = typename __make_unsigned_selector<wchar_t, false, true>::__type;
+    };
+# 1815 "/usr/include/c++/13/type_traits" 3
+  template<>
+    struct __make_unsigned<char16_t>
+    {
+      using __type
+ = typename __make_unsigned_selector<char16_t, false, true>::__type;
+    };
+
+  template<>
+    struct __make_unsigned<char32_t>
+    {
+      using __type
+ = typename __make_unsigned_selector<char32_t, false, true>::__type;
+    };
+
+
+
+
+
+
+  template<typename _Tp>
+    struct make_unsigned
+    { typedef typename __make_unsigned_selector<_Tp>::__type type; };
+
+
+  template<> struct make_unsigned<bool>;
+  template<> struct make_unsigned<bool const>;
+  template<> struct make_unsigned<bool volatile>;
+  template<> struct make_unsigned<bool const volatile>;
+
+
+
+
+  template<typename _Tp>
+    struct __make_signed
+    { typedef _Tp __type; };
+
+  template<>
+    struct __make_signed<char>
+    { typedef signed char __type; };
+
+  template<>
+    struct __make_signed<unsigned char>
+    { typedef signed char __type; };
+
+  template<>
+    struct __make_signed<unsigned short>
+    { typedef signed short __type; };
+
+  template<>
+    struct __make_signed<unsigned int>
+    { typedef signed int __type; };
+
+  template<>
+    struct __make_signed<unsigned long>
+    { typedef signed long __type; };
+
+  template<>
+    struct __make_signed<unsigned long long>
+    { typedef signed long long __type; };
+
+
+  __extension__
+  template<>
+    struct __make_signed<unsigned __int128>
+    { typedef __int128 __type; };
+# 1901 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp,
+    bool _IsInt = is_integral<_Tp>::value,
+    bool _IsEnum = is_enum<_Tp>::value>
+    class __make_signed_selector;
+
+  template<typename _Tp>
+    class __make_signed_selector<_Tp, true, false>
+    {
+      using __signed_type
+ = typename __make_signed<__remove_cv_t<_Tp>>::__type;
+
+    public:
+      using __type
+ = typename __match_cv_qualifiers<_Tp, __signed_type>::__type;
+    };
+
+
+  template<typename _Tp>
+    class __make_signed_selector<_Tp, false, true>
+    {
+      typedef typename __make_unsigned_selector<_Tp>::__type __unsigned_type;
+
+    public:
+      typedef typename __make_signed_selector<__unsigned_type>::__type __type;
+    };
+
+
+
+
+
+  template<>
+    struct __make_signed<wchar_t>
+    {
+      using __type
+ = typename __make_signed_selector<wchar_t, false, true>::__type;
+    };
+# 1947 "/usr/include/c++/13/type_traits" 3
+  template<>
+    struct __make_signed<char16_t>
+    {
+      using __type
+ = typename __make_signed_selector<char16_t, false, true>::__type;
+    };
+
+  template<>
+    struct __make_signed<char32_t>
+    {
+      using __type
+ = typename __make_signed_selector<char32_t, false, true>::__type;
+    };
+
+
+
+
+
+
+  template<typename _Tp>
+    struct make_signed
+    { typedef typename __make_signed_selector<_Tp>::__type type; };
+
+
+  template<> struct make_signed<bool>;
+  template<> struct make_signed<bool const>;
+  template<> struct make_signed<bool volatile>;
+  template<> struct make_signed<bool const volatile>;
+
+
+
+  template<typename _Tp>
+    using make_signed_t = typename make_signed<_Tp>::type;
+
+
+  template<typename _Tp>
+    using make_unsigned_t = typename make_unsigned<_Tp>::type;
+
+
+
+
+
+  template<typename _Tp>
+    struct remove_extent
+    { typedef _Tp type; };
+
+  template<typename _Tp, std::size_t _Size>
+    struct remove_extent<_Tp[_Size]>
+    { typedef _Tp type; };
+
+  template<typename _Tp>
+    struct remove_extent<_Tp[]>
+    { typedef _Tp type; };
+
+
+  template<typename _Tp>
+    struct remove_all_extents
+    { typedef _Tp type; };
+
+  template<typename _Tp, std::size_t _Size>
+    struct remove_all_extents<_Tp[_Size]>
+    { typedef typename remove_all_extents<_Tp>::type type; };
+
+  template<typename _Tp>
+    struct remove_all_extents<_Tp[]>
+    { typedef typename remove_all_extents<_Tp>::type type; };
+
+
+
+  template<typename _Tp>
+    using remove_extent_t = typename remove_extent<_Tp>::type;
+
+
+  template<typename _Tp>
+    using remove_all_extents_t = typename remove_all_extents<_Tp>::type;
+
+
+
+
+  template<typename _Tp, typename>
+    struct __remove_pointer_helper
+    { typedef _Tp type; };
+
+  template<typename _Tp, typename _Up>
+    struct __remove_pointer_helper<_Tp, _Up*>
+    { typedef _Up type; };
+
+
+  template<typename _Tp>
+    struct remove_pointer
+    : public __remove_pointer_helper<_Tp, __remove_cv_t<_Tp>>
+    { };
+
+  template<typename _Tp, typename = void>
+    struct __add_pointer_helper
+    { using type = _Tp; };
+
+  template<typename _Tp>
+    struct __add_pointer_helper<_Tp, __void_t<_Tp*>>
+    { using type = _Tp*; };
+
+
+  template<typename _Tp>
+    struct add_pointer
+    : public __add_pointer_helper<_Tp>
+    { };
+
+  template<typename _Tp>
+    struct add_pointer<_Tp&>
+    { using type = _Tp*; };
+
+  template<typename _Tp>
+    struct add_pointer<_Tp&&>
+    { using type = _Tp*; };
+
+
+
+  template<typename _Tp>
+    using remove_pointer_t = typename remove_pointer<_Tp>::type;
+
+
+  template<typename _Tp>
+    using add_pointer_t = typename add_pointer<_Tp>::type;
+
+
+  template<std::size_t _Len>
+    struct __aligned_storage_msa
+    {
+      union __type
+      {
+ unsigned char __data[_Len];
+ struct __attribute__((__aligned__)) { } __align;
+      };
+    };
+# 2095 "/usr/include/c++/13/type_traits" 3
+  template<std::size_t _Len, std::size_t _Align =
+    __alignof__(typename __aligned_storage_msa<_Len>::__type)>
+    struct
+   
+    aligned_storage
+    {
+      union type
+      {
+ unsigned char __data[_Len];
+ struct __attribute__((__aligned__((_Align)))) { } __align;
+      };
+    };
+
+  template <typename... _Types>
+    struct __strictest_alignment
+    {
+      static const size_t _S_alignment = 0;
+      static const size_t _S_size = 0;
+    };
+
+  template <typename _Tp, typename... _Types>
+    struct __strictest_alignment<_Tp, _Types...>
+    {
+      static const size_t _S_alignment =
+        alignof(_Tp) > __strictest_alignment<_Types...>::_S_alignment
+ ? alignof(_Tp) : __strictest_alignment<_Types...>::_S_alignment;
+      static const size_t _S_size =
+        sizeof(_Tp) > __strictest_alignment<_Types...>::_S_size
+ ? sizeof(_Tp) : __strictest_alignment<_Types...>::_S_size;
+    };
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+# 2141 "/usr/include/c++/13/type_traits" 3
+  template <size_t _Len, typename... _Types>
+    struct
+   
+    aligned_union
+    {
+    private:
+      static_assert(sizeof...(_Types) != 0, "At least one type is required");
+
+      using __strictest = __strictest_alignment<_Types...>;
+      static const size_t _S_len = _Len > __strictest::_S_size
+ ? _Len : __strictest::_S_size;
+    public:
+
+      static const size_t alignment_value = __strictest::_S_alignment;
+
+      typedef typename aligned_storage<_S_len, alignment_value>::type type;
+    };
+
+  template <size_t _Len, typename... _Types>
+    const size_t aligned_union<_Len, _Types...>::alignment_value;
+#pragma GCC diagnostic pop
+
+
+
+
+
+  template<typename _Up>
+    struct __decay_selector
+    : __conditional_t<is_const<const _Up>::value,
+        remove_cv<_Up>,
+        add_pointer<_Up>>
+    { };
+
+  template<typename _Up, size_t _Nm>
+    struct __decay_selector<_Up[_Nm]>
+    { using type = _Up*; };
+
+  template<typename _Up>
+    struct __decay_selector<_Up[]>
+    { using type = _Up*; };
+
+
+
+
+  template<typename _Tp>
+    struct decay
+    { using type = typename __decay_selector<_Tp>::type; };
+
+  template<typename _Tp>
+    struct decay<_Tp&>
+    { using type = typename __decay_selector<_Tp>::type; };
+
+  template<typename _Tp>
+    struct decay<_Tp&&>
+    { using type = typename __decay_selector<_Tp>::type; };
+
+
+
+
+  template<typename _Tp>
+    struct __strip_reference_wrapper
+    {
+      typedef _Tp __type;
+    };
+
+  template<typename _Tp>
+    struct __strip_reference_wrapper<reference_wrapper<_Tp> >
+    {
+      typedef _Tp& __type;
+    };
+
+
+  template<typename _Tp>
+    using __decay_t = typename decay<_Tp>::type;
+
+  template<typename _Tp>
+    using __decay_and_strip = __strip_reference_wrapper<__decay_t<_Tp>>;
+
+
+
+
+
+  template<typename... _Cond>
+    using _Require = __enable_if_t<__and_<_Cond...>::value>;
+
+
+  template<typename _Tp>
+    using __remove_cvref_t
+     = typename remove_cv<typename remove_reference<_Tp>::type>::type;
+
+
+
+
+  template<bool _Cond, typename _Iftrue, typename _Iffalse>
+    struct conditional
+    { typedef _Iftrue type; };
+
+
+  template<typename _Iftrue, typename _Iffalse>
+    struct conditional<false, _Iftrue, _Iffalse>
+    { typedef _Iffalse type; };
+
+
+  template<typename... _Tp>
+    struct common_type;
+# 2256 "/usr/include/c++/13/type_traits" 3
+  template<typename _Tp>
+    struct __success_type
+    { typedef _Tp type; };
+
+  struct __failure_type
+  { };
+
+  struct __do_common_type_impl
+  {
+    template<typename _Tp, typename _Up>
+      using __cond_t
+ = decltype(true ? std::declval<_Tp>() : std::declval<_Up>());
+
+
+
+    template<typename _Tp, typename _Up>
+      static __success_type<__decay_t<__cond_t<_Tp, _Up>>>
+      _S_test(int);
+# 2283 "/usr/include/c++/13/type_traits" 3
+    template<typename, typename>
+      static __failure_type
+      _S_test_2(...);
+
+    template<typename _Tp, typename _Up>
+      static decltype(_S_test_2<_Tp, _Up>(0))
+      _S_test(...);
+  };
+
+
+  template<>
+    struct common_type<>
+    { };
+
+
+  template<typename _Tp0>
+    struct common_type<_Tp0>
+    : public common_type<_Tp0, _Tp0>
+    { };
+
+
+  template<typename _Tp1, typename _Tp2,
+    typename _Dp1 = __decay_t<_Tp1>, typename _Dp2 = __decay_t<_Tp2>>
+    struct __common_type_impl
+    {
+
+
+      using type = common_type<_Dp1, _Dp2>;
+    };
+
+  template<typename _Tp1, typename _Tp2>
+    struct __common_type_impl<_Tp1, _Tp2, _Tp1, _Tp2>
+    : private __do_common_type_impl
+    {
+
+
+      using type = decltype(_S_test<_Tp1, _Tp2>(0));
+    };
+
+
+  template<typename _Tp1, typename _Tp2>
+    struct common_type<_Tp1, _Tp2>
+    : public __common_type_impl<_Tp1, _Tp2>::type
+    { };
+
+  template<typename...>
+    struct __common_type_pack
+    { };
+
+  template<typename, typename, typename = void>
+    struct __common_type_fold;
+
+
+  template<typename _Tp1, typename _Tp2, typename... _Rp>
+    struct common_type<_Tp1, _Tp2, _Rp...>
+    : public __common_type_fold<common_type<_Tp1, _Tp2>,
+    __common_type_pack<_Rp...>>
+    { };
+
+
+
+
+  template<typename _CTp, typename... _Rp>
+    struct __common_type_fold<_CTp, __common_type_pack<_Rp...>,
+         __void_t<typename _CTp::type>>
+    : public common_type<typename _CTp::type, _Rp...>
+    { };
+
+
+  template<typename _CTp, typename _Rp>
+    struct __common_type_fold<_CTp, _Rp, void>
+    { };
+
+  template<typename _Tp, bool = is_enum<_Tp>::value>
+    struct __underlying_type_impl
+    {
+      using type = __underlying_type(_Tp);
+    };
+
+  template<typename _Tp>
+    struct __underlying_type_impl<_Tp, false>
+    { };
+
+
+
+  template<typename _Tp>
+    struct underlying_type
+    : public __underlying_type_impl<_Tp>
+    { };
+
+
+  template<typename _Tp>
+    struct __declval_protector
+    {
+      static const bool __stop = false;
+    };
+
+
+
+
+
+
+  template<typename _Tp>
+    auto declval() noexcept -> decltype(__declval<_Tp>(0))
+    {
+      static_assert(__declval_protector<_Tp>::__stop,
+      "declval() must not be used!");
+      return __declval<_Tp>(0);
+    }
+
+
+  template<typename _Signature>
+    struct result_of;
+
+
+
+
+
+
+  struct __invoke_memfun_ref { };
+  struct __invoke_memfun_deref { };
+  struct __invoke_memobj_ref { };
+  struct __invoke_memobj_deref { };
+  struct __invoke_other { };
+
+
+  template<typename _Tp, typename _Tag>
+    struct __result_of_success : __success_type<_Tp>
+    { using __invoke_type = _Tag; };
+
+
+  struct __result_of_memfun_ref_impl
+  {
+    template<typename _Fp, typename _Tp1, typename... _Args>
+      static __result_of_success<decltype(
+      (std::declval<_Tp1>().*std::declval<_Fp>())(std::declval<_Args>()...)
+      ), __invoke_memfun_ref> _S_test(int);
+
+    template<typename...>
+      static __failure_type _S_test(...);
+  };
+
+  template<typename _MemPtr, typename _Arg, typename... _Args>
+    struct __result_of_memfun_ref
+    : private __result_of_memfun_ref_impl
+    {
+      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
+    };
+
+
+  struct __result_of_memfun_deref_impl
+  {
+    template<typename _Fp, typename _Tp1, typename... _Args>
+      static __result_of_success<decltype(
+      ((*std::declval<_Tp1>()).*std::declval<_Fp>())(std::declval<_Args>()...)
+      ), __invoke_memfun_deref> _S_test(int);
+
+    template<typename...>
+      static __failure_type _S_test(...);
+  };
+
+  template<typename _MemPtr, typename _Arg, typename... _Args>
+    struct __result_of_memfun_deref
+    : private __result_of_memfun_deref_impl
+    {
+      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
+    };
+
+
+  struct __result_of_memobj_ref_impl
+  {
+    template<typename _Fp, typename _Tp1>
+      static __result_of_success<decltype(
+      std::declval<_Tp1>().*std::declval<_Fp>()
+      ), __invoke_memobj_ref> _S_test(int);
+
+    template<typename, typename>
+      static __failure_type _S_test(...);
+  };
+
+  template<typename _MemPtr, typename _Arg>
+    struct __result_of_memobj_ref
+    : private __result_of_memobj_ref_impl
+    {
+      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
+    };
+
+
+  struct __result_of_memobj_deref_impl
+  {
+    template<typename _Fp, typename _Tp1>
+      static __result_of_success<decltype(
+      (*std::declval<_Tp1>()).*std::declval<_Fp>()
+      ), __invoke_memobj_deref> _S_test(int);
+
+    template<typename, typename>
+      static __failure_type _S_test(...);
+  };
+
+  template<typename _MemPtr, typename _Arg>
+    struct __result_of_memobj_deref
+    : private __result_of_memobj_deref_impl
+    {
+      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
+    };
+
+  template<typename _MemPtr, typename _Arg>
+    struct __result_of_memobj;
+
+  template<typename _Res, typename _Class, typename _Arg>
+    struct __result_of_memobj<_Res _Class::*, _Arg>
+    {
+      typedef __remove_cvref_t<_Arg> _Argval;
+      typedef _Res _Class::* _MemPtr;
+      typedef typename __conditional_t<__or_<is_same<_Argval, _Class>,
+        is_base_of<_Class, _Argval>>::value,
+        __result_of_memobj_ref<_MemPtr, _Arg>,
+        __result_of_memobj_deref<_MemPtr, _Arg>
+      >::type type;
+    };
+
+  template<typename _MemPtr, typename _Arg, typename... _Args>
+    struct __result_of_memfun;
+
+  template<typename _Res, typename _Class, typename _Arg, typename... _Args>
+    struct __result_of_memfun<_Res _Class::*, _Arg, _Args...>
+    {
+      typedef typename remove_reference<_Arg>::type _Argval;
+      typedef _Res _Class::* _MemPtr;
+      typedef typename __conditional_t<is_base_of<_Class, _Argval>::value,
+        __result_of_memfun_ref<_MemPtr, _Arg, _Args...>,
+        __result_of_memfun_deref<_MemPtr, _Arg, _Args...>
+      >::type type;
+    };
+
+
+
+
+
+
+  template<typename _Tp, typename _Up = __remove_cvref_t<_Tp>>
+    struct __inv_unwrap
+    {
+      using type = _Tp;
+    };
+
+  template<typename _Tp, typename _Up>
+    struct __inv_unwrap<_Tp, reference_wrapper<_Up>>
+    {
+      using type = _Up&;
+    };
+
+  template<bool, bool, typename _Functor, typename... _ArgTypes>
+    struct __result_of_impl
+    {
+      typedef __failure_type type;
+    };
+
+  template<typename _MemPtr, typename _Arg>
+    struct __result_of_impl<true, false, _MemPtr, _Arg>
+    : public __result_of_memobj<__decay_t<_MemPtr>,
+    typename __inv_unwrap<_Arg>::type>
+    { };
+
+  template<typename _MemPtr, typename _Arg, typename... _Args>
+    struct __result_of_impl<false, true, _MemPtr, _Arg, _Args...>
+    : public __result_of_memfun<__decay_t<_MemPtr>,
+    typename __inv_unwrap<_Arg>::type, _Args...>
+    { };
+
+
+  struct __result_of_other_impl
+  {
+    template<typename _Fn, typename... _Args>
+      static __result_of_success<decltype(
+      std::declval<_Fn>()(std::declval<_Args>()...)
+      ), __invoke_other> _S_test(int);
+
+    template<typename...>
+      static __failure_type _S_test(...);
+  };
+
+  template<typename _Functor, typename... _ArgTypes>
+    struct __result_of_impl<false, false, _Functor, _ArgTypes...>
+    : private __result_of_other_impl
+    {
+      typedef decltype(_S_test<_Functor, _ArgTypes...>(0)) type;
+    };
+
+
+  template<typename _Functor, typename... _ArgTypes>
+    struct __invoke_result
+    : public __result_of_impl<
+        is_member_object_pointer<
+          typename remove_reference<_Functor>::type
+        >::value,
+        is_member_function_pointer<
+          typename remove_reference<_Functor>::type
+        >::value,
+ _Functor, _ArgTypes...
+      >::type
+    { };
+
+
+  template<typename _Functor, typename... _ArgTypes>
+    struct result_of<_Functor(_ArgTypes...)>
+    : public __invoke_result<_Functor, _ArgTypes...>
+    { } __attribute__ ((__deprecated__ ("use '" "std::invoke_result" "' instead")));
+
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+
+  template<size_t _Len, size_t _Align =
+     __alignof__(typename __aligned_storage_msa<_Len>::__type)>
+    using aligned_storage_t = typename aligned_storage<_Len, _Align>::type;
+
+  template <size_t _Len, typename... _Types>
+    using aligned_union_t = typename aligned_union<_Len, _Types...>::type;
+#pragma GCC diagnostic pop
+
+
+  template<typename _Tp>
+    using decay_t = typename decay<_Tp>::type;
+
+
+  template<bool _Cond, typename _Tp = void>
+    using enable_if_t = typename enable_if<_Cond, _Tp>::type;
+
+
+  template<bool _Cond, typename _Iftrue, typename _Iffalse>
+    using conditional_t = typename conditional<_Cond, _Iftrue, _Iffalse>::type;
+
+
+  template<typename... _Tp>
+    using common_type_t = typename common_type<_Tp...>::type;
+
+
+  template<typename _Tp>
+    using underlying_type_t = typename underlying_type<_Tp>::type;
+
+
+  template<typename _Tp>
+    using result_of_t = typename result_of<_Tp>::type;
+
+
+
+
+
+  template<typename...> using void_t = void;
+# 2659 "/usr/include/c++/13/type_traits" 3
+  template<typename _Default, typename _AlwaysVoid,
+    template<typename...> class _Op, typename... _Args>
+    struct __detector
+    {
+      using type = _Default;
+      using __is_detected = false_type;
+    };
+
+
+  template<typename _Default, template<typename...> class _Op,
+     typename... _Args>
+    struct __detector<_Default, __void_t<_Op<_Args...>>, _Op, _Args...>
+    {
+      using type = _Op<_Args...>;
+      using __is_detected = true_type;
+    };
+
+  template<typename _Default, template<typename...> class _Op,
+    typename... _Args>
+    using __detected_or = __detector<_Default, void, _Op, _Args...>;
+
+
+
+  template<typename _Default, template<typename...> class _Op,
+    typename... _Args>
+    using __detected_or_t
+      = typename __detected_or<_Default, _Op, _Args...>::type;
+# 2701 "/usr/include/c++/13/type_traits" 3
+  template <typename _Tp>
+    struct __is_swappable;
+
+  template <typename _Tp>
+    struct __is_nothrow_swappable;
+
+  template<typename>
+    struct __is_tuple_like_impl : false_type
+    { };
+
+
+  template<typename _Tp>
+    struct __is_tuple_like
+    : public __is_tuple_like_impl<__remove_cvref_t<_Tp>>::type
+    { };
+
+
+  template<typename _Tp>
+   
+    inline
+    _Require<__not_<__is_tuple_like<_Tp>>,
+      is_move_constructible<_Tp>,
+      is_move_assignable<_Tp>>
+    swap(_Tp&, _Tp&)
+    noexcept(__and_<is_nothrow_move_constructible<_Tp>,
+             is_nothrow_move_assignable<_Tp>>::value);
+
+  template<typename _Tp, size_t _Nm>
+   
+    inline
+    __enable_if_t<__is_swappable<_Tp>::value>
+    swap(_Tp (&__a)[_Nm], _Tp (&__b)[_Nm])
+    noexcept(__is_nothrow_swappable<_Tp>::value);
+
+
+  namespace __swappable_details {
+    using std::swap;
+
+    struct __do_is_swappable_impl
+    {
+      template<typename _Tp, typename
+               = decltype(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))>
+        static true_type __test(int);
+
+      template<typename>
+        static false_type __test(...);
+    };
+
+    struct __do_is_nothrow_swappable_impl
+    {
+      template<typename _Tp>
+        static __bool_constant<
+          noexcept(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))
+        > __test(int);
+
+      template<typename>
+        static false_type __test(...);
+    };
+
+  }
+
+  template<typename _Tp>
+    struct __is_swappable_impl
+    : public __swappable_details::__do_is_swappable_impl
+    {
+      typedef decltype(__test<_Tp>(0)) type;
+    };
+
+  template<typename _Tp>
+    struct __is_nothrow_swappable_impl
+    : public __swappable_details::__do_is_nothrow_swappable_impl
+    {
+      typedef decltype(__test<_Tp>(0)) type;
+    };
+
+  template<typename _Tp>
+    struct __is_swappable
+    : public __is_swappable_impl<_Tp>::type
+    { };
+
+  template<typename _Tp>
+    struct __is_nothrow_swappable
+    : public __is_nothrow_swappable_impl<_Tp>::type
+    { };
+
+
+
+
+
+
+
+  template<typename _Tp>
+    struct is_swappable
+    : public __is_swappable_impl<_Tp>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    struct is_nothrow_swappable
+    : public __is_nothrow_swappable_impl<_Tp>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+
+  template<typename _Tp>
+    inline constexpr bool is_swappable_v =
+      is_swappable<_Tp>::value;
+
+
+  template<typename _Tp>
+    inline constexpr bool is_nothrow_swappable_v =
+      is_nothrow_swappable<_Tp>::value;
+
+
+
+  namespace __swappable_with_details {
+    using std::swap;
+
+    struct __do_is_swappable_with_impl
+    {
+      template<typename _Tp, typename _Up, typename
+               = decltype(swap(std::declval<_Tp>(), std::declval<_Up>())),
+               typename
+               = decltype(swap(std::declval<_Up>(), std::declval<_Tp>()))>
+        static true_type __test(int);
+
+      template<typename, typename>
+        static false_type __test(...);
+    };
+
+    struct __do_is_nothrow_swappable_with_impl
+    {
+      template<typename _Tp, typename _Up>
+        static __bool_constant<
+          noexcept(swap(std::declval<_Tp>(), std::declval<_Up>()))
+          &&
+          noexcept(swap(std::declval<_Up>(), std::declval<_Tp>()))
+        > __test(int);
+
+      template<typename, typename>
+        static false_type __test(...);
+    };
+
+  }
+
+  template<typename _Tp, typename _Up>
+    struct __is_swappable_with_impl
+    : public __swappable_with_details::__do_is_swappable_with_impl
+    {
+      typedef decltype(__test<_Tp, _Up>(0)) type;
+    };
+
+
+  template<typename _Tp>
+    struct __is_swappable_with_impl<_Tp&, _Tp&>
+    : public __swappable_details::__do_is_swappable_impl
+    {
+      typedef decltype(__test<_Tp&>(0)) type;
+    };
+
+  template<typename _Tp, typename _Up>
+    struct __is_nothrow_swappable_with_impl
+    : public __swappable_with_details::__do_is_nothrow_swappable_with_impl
+    {
+      typedef decltype(__test<_Tp, _Up>(0)) type;
+    };
+
+
+  template<typename _Tp>
+    struct __is_nothrow_swappable_with_impl<_Tp&, _Tp&>
+    : public __swappable_details::__do_is_nothrow_swappable_impl
+    {
+      typedef decltype(__test<_Tp&>(0)) type;
+    };
+
+
+
+  template<typename _Tp, typename _Up>
+    struct is_swappable_with
+    : public __is_swappable_with_impl<_Tp, _Up>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "first template argument must be a complete class or an unbounded array");
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Up>{}),
+ "second template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp, typename _Up>
+    struct is_nothrow_swappable_with
+    : public __is_nothrow_swappable_with_impl<_Tp, _Up>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "first template argument must be a complete class or an unbounded array");
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Up>{}),
+ "second template argument must be a complete class or an unbounded array");
+    };
+
+
+
+  template<typename _Tp, typename _Up>
+    inline constexpr bool is_swappable_with_v =
+      is_swappable_with<_Tp, _Up>::value;
+
+
+  template<typename _Tp, typename _Up>
+    inline constexpr bool is_nothrow_swappable_with_v =
+      is_nothrow_swappable_with<_Tp, _Up>::value;
+# 2924 "/usr/include/c++/13/type_traits" 3
+  template<typename _Result, typename _Ret,
+    bool = is_void<_Ret>::value, typename = void>
+    struct __is_invocable_impl
+    : false_type
+    {
+      using __nothrow_conv = false_type;
+    };
+
+
+  template<typename _Result, typename _Ret>
+    struct __is_invocable_impl<_Result, _Ret,
+                                true,
+          __void_t<typename _Result::type>>
+    : true_type
+    {
+      using __nothrow_conv = true_type;
+    };
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
+
+  template<typename _Result, typename _Ret>
+    struct __is_invocable_impl<_Result, _Ret,
+                                false,
+          __void_t<typename _Result::type>>
+    {
+    private:
+
+      using _Res_t = typename _Result::type;
+
+
+
+      static _Res_t _S_get() noexcept;
+
+
+      template<typename _Tp>
+ static void _S_conv(__type_identity_t<_Tp>) noexcept;
+
+
+      template<typename _Tp,
+        bool _Nothrow = noexcept(_S_conv<_Tp>(_S_get())),
+        typename = decltype(_S_conv<_Tp>(_S_get())),
+
+        bool _Dangle = __reference_converts_from_temporary(_Tp, _Res_t)
+
+
+
+       >
+ static __bool_constant<_Nothrow && !_Dangle>
+ _S_test(int);
+
+      template<typename _Tp, bool = false>
+ static false_type
+ _S_test(...);
+
+    public:
+
+      using type = decltype(_S_test<_Ret, true>(1));
+
+
+      using __nothrow_conv = decltype(_S_test<_Ret>(1));
+    };
+#pragma GCC diagnostic pop
+
+  template<typename _Fn, typename... _ArgTypes>
+    struct __is_invocable
+    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>::type
+    { };
+
+  template<typename _Fn, typename _Tp, typename... _Args>
+    constexpr bool __call_is_nt(__invoke_memfun_ref)
+    {
+      using _Up = typename __inv_unwrap<_Tp>::type;
+      return noexcept((std::declval<_Up>().*std::declval<_Fn>())(
+     std::declval<_Args>()...));
+    }
+
+  template<typename _Fn, typename _Tp, typename... _Args>
+    constexpr bool __call_is_nt(__invoke_memfun_deref)
+    {
+      return noexcept(((*std::declval<_Tp>()).*std::declval<_Fn>())(
+     std::declval<_Args>()...));
+    }
+
+  template<typename _Fn, typename _Tp>
+    constexpr bool __call_is_nt(__invoke_memobj_ref)
+    {
+      using _Up = typename __inv_unwrap<_Tp>::type;
+      return noexcept(std::declval<_Up>().*std::declval<_Fn>());
+    }
+
+  template<typename _Fn, typename _Tp>
+    constexpr bool __call_is_nt(__invoke_memobj_deref)
+    {
+      return noexcept((*std::declval<_Tp>()).*std::declval<_Fn>());
+    }
+
+  template<typename _Fn, typename... _Args>
+    constexpr bool __call_is_nt(__invoke_other)
+    {
+      return noexcept(std::declval<_Fn>()(std::declval<_Args>()...));
+    }
+
+  template<typename _Result, typename _Fn, typename... _Args>
+    struct __call_is_nothrow
+    : __bool_constant<
+ std::__call_is_nt<_Fn, _Args...>(typename _Result::__invoke_type{})
+      >
+    { };
+
+  template<typename _Fn, typename... _Args>
+    using __call_is_nothrow_
+      = __call_is_nothrow<__invoke_result<_Fn, _Args...>, _Fn, _Args...>;
+
+
+  template<typename _Fn, typename... _Args>
+    struct __is_nothrow_invocable
+    : __and_<__is_invocable<_Fn, _Args...>,
+             __call_is_nothrow_<_Fn, _Args...>>::type
+    { };
+
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
+  struct __nonesuchbase {};
+  struct __nonesuch : private __nonesuchbase {
+    ~__nonesuch() = delete;
+    __nonesuch(__nonesuch const&) = delete;
+    void operator=(__nonesuch const&) = delete;
+  };
+#pragma GCC diagnostic pop
+
+
+
+
+
+
+  template<typename _Functor, typename... _ArgTypes>
+    struct invoke_result
+    : public __invoke_result<_Functor, _ArgTypes...>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Functor>{}),
+ "_Functor must be a complete class or an unbounded array");
+      static_assert((std::__is_complete_or_unbounded(
+ __type_identity<_ArgTypes>{}) && ...),
+ "each argument type must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Fn, typename... _Args>
+    using invoke_result_t = typename invoke_result<_Fn, _Args...>::type;
+
+
+  template<typename _Fn, typename... _ArgTypes>
+    struct is_invocable
+    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Fn>{}),
+ "_Fn must be a complete class or an unbounded array");
+      static_assert((std::__is_complete_or_unbounded(
+ __type_identity<_ArgTypes>{}) && ...),
+ "each argument type must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Ret, typename _Fn, typename... _ArgTypes>
+    struct is_invocable_r
+    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, _Ret>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Fn>{}),
+ "_Fn must be a complete class or an unbounded array");
+      static_assert((std::__is_complete_or_unbounded(
+ __type_identity<_ArgTypes>{}) && ...),
+ "each argument type must be a complete class or an unbounded array");
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Ret>{}),
+ "_Ret must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Fn, typename... _ArgTypes>
+    struct is_nothrow_invocable
+    : __and_<__is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>,
+      __call_is_nothrow_<_Fn, _ArgTypes...>>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Fn>{}),
+ "_Fn must be a complete class or an unbounded array");
+      static_assert((std::__is_complete_or_unbounded(
+ __type_identity<_ArgTypes>{}) && ...),
+ "each argument type must be a complete class or an unbounded array");
+    };
+
+
+
+
+
+  template<typename _Result, typename _Ret>
+    using __is_nt_invocable_impl
+      = typename __is_invocable_impl<_Result, _Ret>::__nothrow_conv;
+
+
+
+  template<typename _Ret, typename _Fn, typename... _ArgTypes>
+    struct is_nothrow_invocable_r
+    : __and_<__is_nt_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, _Ret>,
+             __call_is_nothrow_<_Fn, _ArgTypes...>>::type
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Fn>{}),
+ "_Fn must be a complete class or an unbounded array");
+      static_assert((std::__is_complete_or_unbounded(
+ __type_identity<_ArgTypes>{}) && ...),
+ "each argument type must be a complete class or an unbounded array");
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Ret>{}),
+ "_Ret must be a complete class or an unbounded array");
+    };
+# 3155 "/usr/include/c++/13/type_traits" 3
+template <typename _Tp>
+  inline constexpr bool is_void_v = is_void<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_null_pointer_v = is_null_pointer<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_integral_v = is_integral<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_floating_point_v = is_floating_point<_Tp>::value;
+
+template <typename _Tp>
+  inline constexpr bool is_array_v = false;
+template <typename _Tp>
+  inline constexpr bool is_array_v<_Tp[]> = true;
+template <typename _Tp, size_t _Num>
+  inline constexpr bool is_array_v<_Tp[_Num]> = true;
+
+template <typename _Tp>
+  inline constexpr bool is_pointer_v = is_pointer<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_lvalue_reference_v = false;
+template <typename _Tp>
+  inline constexpr bool is_lvalue_reference_v<_Tp&> = true;
+template <typename _Tp>
+  inline constexpr bool is_rvalue_reference_v = false;
+template <typename _Tp>
+  inline constexpr bool is_rvalue_reference_v<_Tp&&> = true;
+template <typename _Tp>
+  inline constexpr bool is_member_object_pointer_v =
+    is_member_object_pointer<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_member_function_pointer_v =
+    is_member_function_pointer<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_enum_v = __is_enum(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_union_v = __is_union(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_class_v = __is_class(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_function_v = is_function<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_reference_v = false;
+template <typename _Tp>
+  inline constexpr bool is_reference_v<_Tp&> = true;
+template <typename _Tp>
+  inline constexpr bool is_reference_v<_Tp&&> = true;
+template <typename _Tp>
+  inline constexpr bool is_arithmetic_v = is_arithmetic<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_fundamental_v = is_fundamental<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_object_v = is_object<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_scalar_v = is_scalar<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_compound_v = is_compound<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_member_pointer_v = is_member_pointer<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_const_v = false;
+template <typename _Tp>
+  inline constexpr bool is_const_v<const _Tp> = true;
+template <typename _Tp>
+  inline constexpr bool is_volatile_v = false;
+template <typename _Tp>
+  inline constexpr bool is_volatile_v<volatile _Tp> = true;
+
+template <typename _Tp>
+  inline constexpr bool is_trivial_v = __is_trivial(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_trivially_copyable_v = __is_trivially_copyable(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_standard_layout_v = __is_standard_layout(_Tp);
+template <typename _Tp>
+ 
+  inline constexpr bool is_pod_v = __is_pod(_Tp);
+template <typename _Tp>
+  [[__deprecated__]]
+  inline constexpr bool is_literal_type_v = __is_literal_type(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_empty_v = __is_empty(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_polymorphic_v = __is_polymorphic(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_abstract_v = __is_abstract(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_final_v = __is_final(_Tp);
+
+template <typename _Tp>
+  inline constexpr bool is_signed_v = is_signed<_Tp>::value;
+template <typename _Tp>
+  inline constexpr bool is_unsigned_v = is_unsigned<_Tp>::value;
+
+template <typename _Tp, typename... _Args>
+  inline constexpr bool is_constructible_v = __is_constructible(_Tp, _Args...);
+template <typename _Tp>
+  inline constexpr bool is_default_constructible_v = __is_constructible(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_copy_constructible_v
+    = __is_constructible(_Tp, __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_move_constructible_v
+    = __is_constructible(_Tp, __add_rval_ref_t<_Tp>);
+
+template <typename _Tp, typename _Up>
+  inline constexpr bool is_assignable_v = __is_assignable(_Tp, _Up);
+template <typename _Tp>
+  inline constexpr bool is_copy_assignable_v
+    = __is_assignable(__add_lval_ref_t<_Tp>, __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_move_assignable_v
+    = __is_assignable(__add_lval_ref_t<_Tp>, __add_rval_ref_t<_Tp>);
+
+template <typename _Tp>
+  inline constexpr bool is_destructible_v = is_destructible<_Tp>::value;
+
+template <typename _Tp, typename... _Args>
+  inline constexpr bool is_trivially_constructible_v
+    = __is_trivially_constructible(_Tp, _Args...);
+template <typename _Tp>
+  inline constexpr bool is_trivially_default_constructible_v
+    = __is_trivially_constructible(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_trivially_copy_constructible_v
+    = __is_trivially_constructible(_Tp, __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_trivially_move_constructible_v
+    = __is_trivially_constructible(_Tp, __add_rval_ref_t<_Tp>);
+
+template <typename _Tp, typename _Up>
+  inline constexpr bool is_trivially_assignable_v
+    = __is_trivially_assignable(_Tp, _Up);
+template <typename _Tp>
+  inline constexpr bool is_trivially_copy_assignable_v
+    = __is_trivially_assignable(__add_lval_ref_t<_Tp>,
+    __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_trivially_move_assignable_v
+    = __is_trivially_assignable(__add_lval_ref_t<_Tp>,
+    __add_rval_ref_t<_Tp>);
+template <typename _Tp>
+  inline constexpr bool is_trivially_destructible_v =
+    is_trivially_destructible<_Tp>::value;
+template <typename _Tp, typename... _Args>
+  inline constexpr bool is_nothrow_constructible_v
+    = __is_nothrow_constructible(_Tp, _Args...);
+template <typename _Tp>
+  inline constexpr bool is_nothrow_default_constructible_v
+    = __is_nothrow_constructible(_Tp);
+template <typename _Tp>
+  inline constexpr bool is_nothrow_copy_constructible_v
+    = __is_nothrow_constructible(_Tp, __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_nothrow_move_constructible_v
+    = __is_nothrow_constructible(_Tp, __add_rval_ref_t<_Tp>);
+
+template <typename _Tp, typename _Up>
+  inline constexpr bool is_nothrow_assignable_v
+    = __is_nothrow_assignable(_Tp, _Up);
+template <typename _Tp>
+  inline constexpr bool is_nothrow_copy_assignable_v
+    = __is_nothrow_assignable(__add_lval_ref_t<_Tp>,
+         __add_lval_ref_t<const _Tp>);
+template <typename _Tp>
+  inline constexpr bool is_nothrow_move_assignable_v
+    = __is_nothrow_assignable(__add_lval_ref_t<_Tp>, __add_rval_ref_t<_Tp>);
+
+template <typename _Tp>
+  inline constexpr bool is_nothrow_destructible_v =
+    is_nothrow_destructible<_Tp>::value;
+
+template <typename _Tp>
+  inline constexpr bool has_virtual_destructor_v
+    = __has_virtual_destructor(_Tp);
+
+template <typename _Tp>
+  inline constexpr size_t alignment_of_v = alignment_of<_Tp>::value;
+
+template <typename _Tp>
+  inline constexpr size_t rank_v = 0;
+template <typename _Tp, size_t _Size>
+  inline constexpr size_t rank_v<_Tp[_Size]> = 1 + rank_v<_Tp>;
+template <typename _Tp>
+  inline constexpr size_t rank_v<_Tp[]> = 1 + rank_v<_Tp>;
+
+template <typename _Tp, unsigned _Idx = 0>
+  inline constexpr size_t extent_v = 0;
+template <typename _Tp, size_t _Size>
+  inline constexpr size_t extent_v<_Tp[_Size], 0> = _Size;
+template <typename _Tp, unsigned _Idx, size_t _Size>
+  inline constexpr size_t extent_v<_Tp[_Size], _Idx> = extent_v<_Tp, _Idx - 1>;
+template <typename _Tp>
+  inline constexpr size_t extent_v<_Tp[], 0> = 0;
+template <typename _Tp, unsigned _Idx>
+  inline constexpr size_t extent_v<_Tp[], _Idx> = extent_v<_Tp, _Idx - 1>;
+
+
+template <typename _Tp, typename _Up>
+  inline constexpr bool is_same_v = __is_same(_Tp, _Up);
+
+
+
+
+
+
+template <typename _Base, typename _Derived>
+  inline constexpr bool is_base_of_v = __is_base_of(_Base, _Derived);
+
+template <typename _From, typename _To>
+  inline constexpr bool is_convertible_v = __is_convertible(_From, _To);
+
+
+
+
+template<typename _Fn, typename... _Args>
+  inline constexpr bool is_invocable_v = is_invocable<_Fn, _Args...>::value;
+template<typename _Fn, typename... _Args>
+  inline constexpr bool is_nothrow_invocable_v
+    = is_nothrow_invocable<_Fn, _Args...>::value;
+template<typename _Ret, typename _Fn, typename... _Args>
+  inline constexpr bool is_invocable_r_v
+    = is_invocable_r<_Ret, _Fn, _Args...>::value;
+template<typename _Ret, typename _Fn, typename... _Args>
+  inline constexpr bool is_nothrow_invocable_r_v
+    = is_nothrow_invocable_r<_Ret, _Fn, _Args...>::value;
+
+
+
+
+
+
+  template<typename _Tp>
+    struct has_unique_object_representations
+    : bool_constant<__has_unique_object_representations(
+      remove_cv_t<remove_all_extents_t<_Tp>>
+      )>
+    {
+      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
+ "template argument must be a complete class or an unbounded array");
+    };
+
+
+  template<typename _Tp>
+    inline constexpr bool has_unique_object_representations_v
+      = has_unique_object_representations<_Tp>::value;
+
+
+
+
+
+
+  template<typename _Tp>
+    struct is_aggregate
+    : bool_constant<__is_aggregate(remove_cv_t<_Tp>)>
+    { };
+
+
+
+
+
+  template<typename _Tp>
+    inline constexpr bool is_aggregate_v = __is_aggregate(remove_cv_t<_Tp>);
+# 3833 "/usr/include/c++/13/type_traits" 3
+
+}
+# 61 "/usr/include/c++/13/bits/stl_pair.h" 2 3
+# 1 "/usr/include/c++/13/bits/move.h" 1 3
+# 40 "/usr/include/c++/13/bits/move.h" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+
+
+
+  template<typename _Tp>
+    inline constexpr _Tp*
+    __addressof(_Tp& __r) noexcept
+    { return __builtin_addressof(__r); }
+# 67 "/usr/include/c++/13/bits/move.h" 3
+  template<typename _Tp>
+    [[__nodiscard__]]
+    constexpr _Tp&&
+    forward(typename std::remove_reference<_Tp>::type& __t) noexcept
+    { return static_cast<_Tp&&>(__t); }
+
+
+
+
+
+
+
+  template<typename _Tp>
+    [[__nodiscard__]]
+    constexpr _Tp&&
+    forward(typename std::remove_reference<_Tp>::type&& __t) noexcept
+    {
+      static_assert(!std::is_lvalue_reference<_Tp>::value,
+   "std::forward must not be used to convert an rvalue to an lvalue");
+      return static_cast<_Tp&&>(__t);
+    }
+
+
+
+
+
+
+  template<typename _Tp>
+    [[__nodiscard__]]
+    constexpr typename std::remove_reference<_Tp>::type&&
+    move(_Tp&& __t) noexcept
+    { return static_cast<typename std::remove_reference<_Tp>::type&&>(__t); }
+
+
+  template<typename _Tp>
+    struct __move_if_noexcept_cond
+    : public __and_<__not_<is_nothrow_move_constructible<_Tp>>,
+                    is_copy_constructible<_Tp>>::type { };
+# 114 "/usr/include/c++/13/bits/move.h" 3
+  template<typename _Tp>
+    [[__nodiscard__]]
+    constexpr
+    __conditional_t<__move_if_noexcept_cond<_Tp>::value, const _Tp&, _Tp&&>
+    move_if_noexcept(_Tp& __x) noexcept
+    { return std::move(__x); }
+# 135 "/usr/include/c++/13/bits/move.h" 3
+  template<typename _Tp>
+    [[__nodiscard__]]
+    inline constexpr _Tp*
+    addressof(_Tp& __r) noexcept
+    { return std::__addressof(__r); }
+
+
+
+  template<typename _Tp>
+    const _Tp* addressof(const _Tp&&) = delete;
+
+
+  template <typename _Tp, typename _Up = _Tp>
+   
+    inline _Tp
+    __exchange(_Tp& __obj, _Up&& __new_val)
+    {
+      _Tp __old_val = std::move(__obj);
+      __obj = std::forward<_Up>(__new_val);
+      return __old_val;
+    }
+# 179 "/usr/include/c++/13/bits/move.h" 3
+  template<typename _Tp>
+   
+    inline
+
+    typename enable_if<__and_<__not_<__is_tuple_like<_Tp>>,
+         is_move_constructible<_Tp>,
+         is_move_assignable<_Tp>>::value>::type
+
+
+
+    swap(_Tp& __a, _Tp& __b)
+    noexcept(__and_<is_nothrow_move_constructible<_Tp>, is_nothrow_move_assignable<_Tp>>::value)
+
+    {
+
+
+
+
+      _Tp __tmp = std::move(__a);
+      __a = std::move(__b);
+      __b = std::move(__tmp);
+    }
+
+
+
+
+  template<typename _Tp, size_t _Nm>
+   
+    inline
+
+    typename enable_if<__is_swappable<_Tp>::value>::type
+
+
+
+    swap(_Tp (&__a)[_Nm], _Tp (&__b)[_Nm])
+    noexcept(__is_nothrow_swappable<_Tp>::value)
+    {
+      for (size_t __n = 0; __n < _Nm; ++__n)
+ swap(__a[__n], __b[__n]);
+    }
+
+
+
+}
+# 62 "/usr/include/c++/13/bits/stl_pair.h" 2 3
+# 1 "/usr/include/c++/13/bits/utility.h" 1 3
+# 36 "/usr/include/c++/13/bits/utility.h" 3
+       
+# 37 "/usr/include/c++/13/bits/utility.h" 3
+
+
+
+
+
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+  template<typename _Tp>
+    struct tuple_size;
+
+
+
+
+
+  template<typename _Tp,
+    typename _Up = typename remove_cv<_Tp>::type,
+    typename = typename enable_if<is_same<_Tp, _Up>::value>::type,
+    size_t = tuple_size<_Tp>::value>
+    using __enable_if_has_tuple_size = _Tp;
+
+  template<typename _Tp>
+    struct tuple_size<const __enable_if_has_tuple_size<_Tp>>
+    : public tuple_size<_Tp> { };
+
+  template<typename _Tp>
+    struct tuple_size<volatile __enable_if_has_tuple_size<_Tp>>
+    : public tuple_size<_Tp> { };
+
+  template<typename _Tp>
+    struct tuple_size<const volatile __enable_if_has_tuple_size<_Tp>>
+    : public tuple_size<_Tp> { };
+
+
+  template<typename _Tp>
+    inline constexpr size_t tuple_size_v = tuple_size<_Tp>::value;
+
+
+
+  template<size_t __i, typename _Tp>
+    struct tuple_element;
+
+
+  template<size_t __i, typename _Tp>
+    using __tuple_element_t = typename tuple_element<__i, _Tp>::type;
+
+  template<size_t __i, typename _Tp>
+    struct tuple_element<__i, const _Tp>
+    {
+      using type = const __tuple_element_t<__i, _Tp>;
+    };
+
+  template<size_t __i, typename _Tp>
+    struct tuple_element<__i, volatile _Tp>
+    {
+      using type = volatile __tuple_element_t<__i, _Tp>;
+    };
+
+  template<size_t __i, typename _Tp>
+    struct tuple_element<__i, const volatile _Tp>
+    {
+      using type = const volatile __tuple_element_t<__i, _Tp>;
+    };
+
+
+
+
+
+  template<typename _Tp, typename... _Types>
+    constexpr size_t
+    __find_uniq_type_in_pack()
+    {
+      constexpr size_t __sz = sizeof...(_Types);
+      constexpr bool __found[__sz] = { __is_same(_Tp, _Types) ... };
+      size_t __n = __sz;
+      for (size_t __i = 0; __i < __sz; ++__i)
+ {
+   if (__found[__i])
+     {
+       if (__n < __sz)
+  return __sz;
+       __n = __i;
+     }
+ }
+      return __n;
+    }
+# 134 "/usr/include/c++/13/bits/utility.h" 3
+  template<size_t __i, typename _Tp>
+    using tuple_element_t = typename tuple_element<__i, _Tp>::type;
+
+
+
+
+  template<size_t... _Indexes> struct _Index_tuple { };
+
+
+  template<size_t _Num>
+    struct _Build_index_tuple
+    {
+# 154 "/usr/include/c++/13/bits/utility.h" 3
+      using __type = _Index_tuple<__integer_pack(_Num)...>;
+
+    };
+
+
+
+
+
+
+  template<typename _Tp, _Tp... _Idx>
+    struct integer_sequence
+    {
+
+
+
+      typedef _Tp value_type;
+      static constexpr size_t size() noexcept { return sizeof...(_Idx); }
+    };
+
+
+  template<typename _Tp, _Tp _Num>
+    using make_integer_sequence
+
+
+
+      = integer_sequence<_Tp, __integer_pack(_Tp(_Num))...>;
+
+
+
+  template<size_t... _Idx>
+    using index_sequence = integer_sequence<size_t, _Idx...>;
+
+
+  template<size_t _Num>
+    using make_index_sequence = make_integer_sequence<size_t, _Num>;
+
+
+  template<typename... _Types>
+    using index_sequence_for = make_index_sequence<sizeof...(_Types)>;
+
+
+
+  struct in_place_t {
+    explicit in_place_t() = default;
+  };
+
+  inline constexpr in_place_t in_place{};
+
+  template<typename _Tp> struct in_place_type_t
+  {
+    explicit in_place_type_t() = default;
+  };
+
+  template<typename _Tp>
+    inline constexpr in_place_type_t<_Tp> in_place_type{};
+
+  template<size_t _Idx> struct in_place_index_t
+  {
+    explicit in_place_index_t() = default;
+  };
+
+  template<size_t _Idx>
+    inline constexpr in_place_index_t<_Idx> in_place_index{};
+
+  template<typename>
+    inline constexpr bool __is_in_place_type_v = false;
+
+  template<typename _Tp>
+    inline constexpr bool __is_in_place_type_v<in_place_type_t<_Tp>> = true;
+
+  template<typename _Tp>
+    using __is_in_place_type = bool_constant<__is_in_place_type_v<_Tp>>;
+
+
+
+
+  template<size_t _Np, typename... _Types>
+    struct _Nth_type
+    { };
+
+  template<typename _Tp0, typename... _Rest>
+    struct _Nth_type<0, _Tp0, _Rest...>
+    { using type = _Tp0; };
+
+  template<typename _Tp0, typename _Tp1, typename... _Rest>
+    struct _Nth_type<1, _Tp0, _Tp1, _Rest...>
+    { using type = _Tp1; };
+
+  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
+    struct _Nth_type<2, _Tp0, _Tp1, _Tp2, _Rest...>
+    { using type = _Tp2; };
+
+  template<size_t _Np, typename _Tp0, typename _Tp1, typename _Tp2,
+    typename... _Rest>
+
+
+
+    struct _Nth_type<_Np, _Tp0, _Tp1, _Tp2, _Rest...>
+    : _Nth_type<_Np - 3, _Rest...>
+    { };
+
+
+  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
+    struct _Nth_type<0, _Tp0, _Tp1, _Tp2, _Rest...>
+    { using type = _Tp0; };
+
+  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
+    struct _Nth_type<1, _Tp0, _Tp1, _Tp2, _Rest...>
+    { using type = _Tp1; };
+
+
+
+
+
+
+
+}
+# 63 "/usr/include/c++/13/bits/stl_pair.h" 2 3
+
+
+
+
+
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 80 "/usr/include/c++/13/bits/stl_pair.h" 3
+  struct piecewise_construct_t { explicit piecewise_construct_t() = default; };
+
+
+  inline constexpr piecewise_construct_t piecewise_construct =
+    piecewise_construct_t();
+
+
+
+
+  template<typename...>
+    class tuple;
+
+  template<size_t...>
+    struct _Index_tuple;
+
+
+
+
+
+
+
+  template <bool, typename _T1, typename _T2>
+    struct _PCC
+    {
+      template <typename _U1, typename _U2>
+      static constexpr bool _ConstructiblePair()
+      {
+ return __and_<is_constructible<_T1, const _U1&>,
+        is_constructible<_T2, const _U2&>>::value;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _ImplicitlyConvertiblePair()
+      {
+ return __and_<is_convertible<const _U1&, _T1>,
+        is_convertible<const _U2&, _T2>>::value;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _MoveConstructiblePair()
+      {
+ return __and_<is_constructible<_T1, _U1&&>,
+        is_constructible<_T2, _U2&&>>::value;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _ImplicitlyMoveConvertiblePair()
+      {
+ return __and_<is_convertible<_U1&&, _T1>,
+        is_convertible<_U2&&, _T2>>::value;
+      }
+    };
+
+  template <typename _T1, typename _T2>
+    struct _PCC<false, _T1, _T2>
+    {
+      template <typename _U1, typename _U2>
+      static constexpr bool _ConstructiblePair()
+      {
+ return false;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _ImplicitlyConvertiblePair()
+      {
+ return false;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _MoveConstructiblePair()
+      {
+ return false;
+      }
+
+      template <typename _U1, typename _U2>
+      static constexpr bool _ImplicitlyMoveConvertiblePair()
+      {
+ return false;
+      }
+    };
+
+
+
+  template<typename _U1, typename _U2> class __pair_base
+  {
+
+    template<typename _T1, typename _T2> friend struct pair;
+    __pair_base() = default;
+    ~__pair_base() = default;
+    __pair_base(const __pair_base&) = default;
+    __pair_base& operator=(const __pair_base&) = delete;
+
+  };
+# 186 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    struct pair
+    : public __pair_base<_T1, _T2>
+    {
+      typedef _T1 first_type;
+      typedef _T2 second_type;
+
+      _T1 first;
+      _T2 second;
+
+
+      constexpr pair(const pair&) = default;
+      constexpr pair(pair&&) = default;
+
+      template<typename... _Args1, typename... _Args2>
+
+ pair(piecewise_construct_t, tuple<_Args1...>, tuple<_Args2...>);
+
+
+      void
+      swap(pair& __p)
+      noexcept(__and_<__is_nothrow_swappable<_T1>,
+        __is_nothrow_swappable<_T2>>::value)
+      {
+ using std::swap;
+ swap(first, __p.first);
+ swap(second, __p.second);
+      }
+# 234 "/usr/include/c++/13/bits/stl_pair.h" 3
+    private:
+      template<typename... _Args1, size_t... _Indexes1,
+        typename... _Args2, size_t... _Indexes2>
+
+ pair(tuple<_Args1...>&, tuple<_Args2...>&,
+      _Index_tuple<_Indexes1...>, _Index_tuple<_Indexes2...>);
+    public:
+# 525 "/usr/include/c++/13/bits/stl_pair.h" 3
+      template <typename _U1 = _T1,
+                typename _U2 = _T2,
+                typename enable_if<__and_<
+                                     __is_implicitly_default_constructible<_U1>,
+                                     __is_implicitly_default_constructible<_U2>>
+                                   ::value, bool>::type = true>
+      constexpr pair()
+      : first(), second() { }
+
+      template <typename _U1 = _T1,
+                typename _U2 = _T2,
+                typename enable_if<__and_<
+                       is_default_constructible<_U1>,
+                       is_default_constructible<_U2>,
+                       __not_<
+                         __and_<__is_implicitly_default_constructible<_U1>,
+                                __is_implicitly_default_constructible<_U2>>>>
+                                   ::value, bool>::type = false>
+      explicit constexpr pair()
+      : first(), second() { }
+
+
+
+      using _PCCP = _PCC<true, _T1, _T2>;
+
+
+
+      template<typename _U1 = _T1, typename _U2=_T2, typename
+        enable_if<_PCCP::template
+      _ConstructiblePair<_U1, _U2>()
+                  && _PCCP::template
+      _ImplicitlyConvertiblePair<_U1, _U2>(),
+                         bool>::type=true>
+      constexpr pair(const _T1& __a, const _T2& __b)
+      : first(__a), second(__b) { }
+
+
+       template<typename _U1 = _T1, typename _U2=_T2, typename
+  enable_if<_PCCP::template
+       _ConstructiblePair<_U1, _U2>()
+                   && !_PCCP::template
+       _ImplicitlyConvertiblePair<_U1, _U2>(),
+                         bool>::type=false>
+      explicit constexpr pair(const _T1& __a, const _T2& __b)
+      : first(__a), second(__b) { }
+
+
+
+      template <typename _U1, typename _U2>
+        using _PCCFP = _PCC<!is_same<_T1, _U1>::value
+       || !is_same<_T2, _U2>::value,
+       _T1, _T2>;
+
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCFP<_U1, _U2>::template
+      _ConstructiblePair<_U1, _U2>()
+                  && _PCCFP<_U1, _U2>::template
+      _ImplicitlyConvertiblePair<_U1, _U2>(),
+     bool>::type=true>
+ constexpr pair(const pair<_U1, _U2>& __p)
+ : first(__p.first), second(__p.second)
+ { ; }
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCFP<_U1, _U2>::template
+      _ConstructiblePair<_U1, _U2>()
+    && !_PCCFP<_U1, _U2>::template
+      _ImplicitlyConvertiblePair<_U1, _U2>(),
+                         bool>::type=false>
+ explicit constexpr pair(const pair<_U1, _U2>& __p)
+ : first(__p.first), second(__p.second)
+ { ; }
+# 609 "/usr/include/c++/13/bits/stl_pair.h" 3
+    private:
+
+
+
+      struct __zero_as_null_pointer_constant
+      {
+ __zero_as_null_pointer_constant(int __zero_as_null_pointer_constant::*)
+ { }
+ template<typename _Tp,
+   typename = __enable_if_t<is_null_pointer<_Tp>::value>>
+ __zero_as_null_pointer_constant(_Tp) = delete;
+      };
+
+    public:
+
+
+
+
+      template<typename _U1,
+        __enable_if_t<__and_<__not_<is_reference<_U1>>,
+        is_pointer<_T2>,
+        is_constructible<_T1, _U1>,
+        __not_<is_constructible<_T1, const _U1&>>,
+        is_convertible<_U1, _T1>>::value,
+        bool> = true>
+ __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
+ constexpr
+ pair(_U1&& __x, __zero_as_null_pointer_constant, ...)
+ : first(std::forward<_U1>(__x)), second(nullptr)
+ { ; }
+
+      template<typename _U1,
+        __enable_if_t<__and_<__not_<is_reference<_U1>>,
+        is_pointer<_T2>,
+        is_constructible<_T1, _U1>,
+        __not_<is_constructible<_T1, const _U1&>>,
+        __not_<is_convertible<_U1, _T1>>>::value,
+        bool> = false>
+ __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
+ explicit constexpr
+ pair(_U1&& __x, __zero_as_null_pointer_constant, ...)
+ : first(std::forward<_U1>(__x)), second(nullptr)
+ { ; }
+
+      template<typename _U2,
+        __enable_if_t<__and_<is_pointer<_T1>,
+        __not_<is_reference<_U2>>,
+        is_constructible<_T2, _U2>,
+        __not_<is_constructible<_T2, const _U2&>>,
+        is_convertible<_U2, _T2>>::value,
+        bool> = true>
+ __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
+ constexpr
+ pair(__zero_as_null_pointer_constant, _U2&& __y, ...)
+ : first(nullptr), second(std::forward<_U2>(__y))
+ { ; }
+
+      template<typename _U2,
+        __enable_if_t<__and_<is_pointer<_T1>,
+        __not_<is_reference<_U2>>,
+        is_constructible<_T2, _U2>,
+        __not_<is_constructible<_T2, const _U2&>>,
+        __not_<is_convertible<_U2, _T2>>>::value,
+        bool> = false>
+ __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
+ explicit constexpr
+ pair(__zero_as_null_pointer_constant, _U2&& __y, ...)
+ : first(nullptr), second(std::forward<_U2>(__y))
+ { ; }
+
+
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCP::template
+      _MoveConstructiblePair<_U1, _U2>()
+     && _PCCP::template
+      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
+                         bool>::type=true>
+ constexpr pair(_U1&& __x, _U2&& __y)
+ : first(std::forward<_U1>(__x)), second(std::forward<_U2>(__y))
+ { ; }
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCP::template
+      _MoveConstructiblePair<_U1, _U2>()
+     && !_PCCP::template
+      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
+                         bool>::type=false>
+ explicit constexpr pair(_U1&& __x, _U2&& __y)
+ : first(std::forward<_U1>(__x)), second(std::forward<_U2>(__y))
+ { ; }
+
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCFP<_U1, _U2>::template
+      _MoveConstructiblePair<_U1, _U2>()
+     && _PCCFP<_U1, _U2>::template
+      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
+                         bool>::type=true>
+ constexpr pair(pair<_U1, _U2>&& __p)
+ : first(std::forward<_U1>(__p.first)),
+   second(std::forward<_U2>(__p.second))
+ { ; }
+
+      template<typename _U1, typename _U2, typename
+        enable_if<_PCCFP<_U1, _U2>::template
+      _MoveConstructiblePair<_U1, _U2>()
+     && !_PCCFP<_U1, _U2>::template
+      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
+                         bool>::type=false>
+ explicit constexpr pair(pair<_U1, _U2>&& __p)
+ : first(std::forward<_U1>(__p.first)),
+   second(std::forward<_U2>(__p.second))
+ { ; }
+
+
+
+      pair&
+      operator=(__conditional_t<__and_<is_copy_assignable<_T1>,
+           is_copy_assignable<_T2>>::value,
+    const pair&, const __nonesuch&> __p)
+      {
+ first = __p.first;
+ second = __p.second;
+ return *this;
+      }
+
+      pair&
+      operator=(__conditional_t<__and_<is_move_assignable<_T1>,
+           is_move_assignable<_T2>>::value,
+    pair&&, __nonesuch&&> __p)
+      noexcept(__and_<is_nothrow_move_assignable<_T1>,
+        is_nothrow_move_assignable<_T2>>::value)
+      {
+ first = std::forward<first_type>(__p.first);
+ second = std::forward<second_type>(__p.second);
+ return *this;
+      }
+
+      template<typename _U1, typename _U2>
+ typename enable_if<__and_<is_assignable<_T1&, const _U1&>,
+      is_assignable<_T2&, const _U2&>>::value,
+      pair&>::type
+ operator=(const pair<_U1, _U2>& __p)
+ {
+   first = __p.first;
+   second = __p.second;
+   return *this;
+ }
+
+      template<typename _U1, typename _U2>
+ typename enable_if<__and_<is_assignable<_T1&, _U1&&>,
+      is_assignable<_T2&, _U2&&>>::value,
+      pair&>::type
+ operator=(pair<_U1, _U2>&& __p)
+ {
+   first = std::forward<_U1>(__p.first);
+   second = std::forward<_U2>(__p.second);
+   return *this;
+ }
+# 801 "/usr/include/c++/13/bits/stl_pair.h" 3
+    };
+
+
+
+
+  template<typename _T1, typename _T2> pair(_T1, _T2) -> pair<_T1, _T2>;
+
+
+
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator==(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return __x.first == __y.first && __x.second == __y.second; }
+# 833 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return __x.first < __y.first
+      || (!(__y.first < __x.first) && __x.second < __y.second); }
+
+
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator!=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return !(__x == __y); }
+
+
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator>(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return __y < __x; }
+
+
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator<=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return !(__y < __x); }
+
+
+  template<typename _T1, typename _T2>
+    inline constexpr bool
+    operator>=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
+    { return !(__x < __y); }
+# 870 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    inline
+
+
+    typename enable_if<__and_<__is_swappable<_T1>,
+                              __is_swappable<_T2>>::value>::type
+
+
+
+    swap(pair<_T1, _T2>& __x, pair<_T1, _T2>& __y)
+    noexcept(noexcept(__x.swap(__y)))
+    { __x.swap(__y); }
+# 893 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    typename enable_if<!__and_<__is_swappable<_T1>,
+          __is_swappable<_T2>>::value>::type
+    swap(pair<_T1, _T2>&, pair<_T1, _T2>&) = delete;
+# 919 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    constexpr pair<typename __decay_and_strip<_T1>::__type,
+                   typename __decay_and_strip<_T2>::__type>
+    make_pair(_T1&& __x, _T2&& __y)
+    {
+      typedef typename __decay_and_strip<_T1>::__type __ds_type1;
+      typedef typename __decay_and_strip<_T2>::__type __ds_type2;
+      typedef pair<__ds_type1, __ds_type2> __pair_type;
+      return __pair_type(std::forward<_T1>(__x), std::forward<_T2>(__y));
+    }
+# 942 "/usr/include/c++/13/bits/stl_pair.h" 3
+  template<typename _T1, typename _T2>
+    struct __is_tuple_like_impl<pair<_T1, _T2>> : true_type
+    { };
+
+
+
+  template<class _Tp1, class _Tp2>
+    struct tuple_size<pair<_Tp1, _Tp2>>
+    : public integral_constant<size_t, 2> { };
+
+
+  template<class _Tp1, class _Tp2>
+    struct tuple_element<0, pair<_Tp1, _Tp2>>
+    { typedef _Tp1 type; };
+
+
+  template<class _Tp1, class _Tp2>
+    struct tuple_element<1, pair<_Tp1, _Tp2>>
+    { typedef _Tp2 type; };
+
+
+  template<typename _Tp1, typename _Tp2>
+    inline constexpr size_t tuple_size_v<pair<_Tp1, _Tp2>> = 2;
+
+  template<typename _Tp1, typename _Tp2>
+    inline constexpr size_t tuple_size_v<const pair<_Tp1, _Tp2>> = 2;
+
+  template<typename _Tp>
+    inline constexpr bool __is_pair = false;
+
+  template<typename _Tp, typename _Up>
+    inline constexpr bool __is_pair<pair<_Tp, _Up>> = true;
+
+
+
+  template<size_t _Int>
+    struct __pair_get;
+
+  template<>
+    struct __pair_get<0>
+    {
+      template<typename _Tp1, typename _Tp2>
+ static constexpr _Tp1&
+ __get(pair<_Tp1, _Tp2>& __pair) noexcept
+ { return __pair.first; }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr _Tp1&&
+ __move_get(pair<_Tp1, _Tp2>&& __pair) noexcept
+ { return std::forward<_Tp1>(__pair.first); }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr const _Tp1&
+ __const_get(const pair<_Tp1, _Tp2>& __pair) noexcept
+ { return __pair.first; }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr const _Tp1&&
+ __const_move_get(const pair<_Tp1, _Tp2>&& __pair) noexcept
+ { return std::forward<const _Tp1>(__pair.first); }
+    };
+
+  template<>
+    struct __pair_get<1>
+    {
+      template<typename _Tp1, typename _Tp2>
+ static constexpr _Tp2&
+ __get(pair<_Tp1, _Tp2>& __pair) noexcept
+ { return __pair.second; }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr _Tp2&&
+ __move_get(pair<_Tp1, _Tp2>&& __pair) noexcept
+ { return std::forward<_Tp2>(__pair.second); }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr const _Tp2&
+ __const_get(const pair<_Tp1, _Tp2>& __pair) noexcept
+ { return __pair.second; }
+
+      template<typename _Tp1, typename _Tp2>
+ static constexpr const _Tp2&&
+ __const_move_get(const pair<_Tp1, _Tp2>&& __pair) noexcept
+ { return std::forward<const _Tp2>(__pair.second); }
+    };
+
+
+
+
+
+
+  template<size_t _Int, class _Tp1, class _Tp2>
+    constexpr typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&
+    get(pair<_Tp1, _Tp2>& __in) noexcept
+    { return __pair_get<_Int>::__get(__in); }
+
+  template<size_t _Int, class _Tp1, class _Tp2>
+    constexpr typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&&
+    get(pair<_Tp1, _Tp2>&& __in) noexcept
+    { return __pair_get<_Int>::__move_get(std::move(__in)); }
+
+  template<size_t _Int, class _Tp1, class _Tp2>
+    constexpr const typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&
+    get(const pair<_Tp1, _Tp2>& __in) noexcept
+    { return __pair_get<_Int>::__const_get(__in); }
+
+  template<size_t _Int, class _Tp1, class _Tp2>
+    constexpr const typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&&
+    get(const pair<_Tp1, _Tp2>&& __in) noexcept
+    { return __pair_get<_Int>::__const_move_get(std::move(__in)); }
+
+
+
+
+
+  template <typename _Tp, typename _Up>
+    constexpr _Tp&
+    get(pair<_Tp, _Up>& __p) noexcept
+    { return __p.first; }
+
+  template <typename _Tp, typename _Up>
+    constexpr const _Tp&
+    get(const pair<_Tp, _Up>& __p) noexcept
+    { return __p.first; }
+
+  template <typename _Tp, typename _Up>
+    constexpr _Tp&&
+    get(pair<_Tp, _Up>&& __p) noexcept
+    { return std::move(__p.first); }
+
+  template <typename _Tp, typename _Up>
+    constexpr const _Tp&&
+    get(const pair<_Tp, _Up>&& __p) noexcept
+    { return std::move(__p.first); }
+
+  template <typename _Tp, typename _Up>
+    constexpr _Tp&
+    get(pair<_Up, _Tp>& __p) noexcept
+    { return __p.second; }
+
+  template <typename _Tp, typename _Up>
+    constexpr const _Tp&
+    get(const pair<_Up, _Tp>& __p) noexcept
+    { return __p.second; }
+
+  template <typename _Tp, typename _Up>
+    constexpr _Tp&&
+    get(pair<_Up, _Tp>&& __p) noexcept
+    { return std::move(__p.second); }
+
+  template <typename _Tp, typename _Up>
+    constexpr const _Tp&&
+    get(const pair<_Up, _Tp>&& __p) noexcept
+    { return std::move(__p.second); }
+# 1118 "/usr/include/c++/13/bits/stl_pair.h" 3
+
+}
+# 65 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+# 1 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 1 3
+# 62 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+       
+# 63 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+# 74 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 93 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+  struct input_iterator_tag { };
+
+
+  struct output_iterator_tag { };
+
+
+  struct forward_iterator_tag : public input_iterator_tag { };
+
+
+
+  struct bidirectional_iterator_tag : public forward_iterator_tag { };
+
+
+
+  struct random_access_iterator_tag : public bidirectional_iterator_tag { };
+# 125 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+  template<typename _Category, typename _Tp, typename _Distance = ptrdiff_t,
+           typename _Pointer = _Tp*, typename _Reference = _Tp&>
+    struct [[__deprecated__]] iterator
+    {
+
+      typedef _Category iterator_category;
+
+      typedef _Tp value_type;
+
+      typedef _Distance difference_type;
+
+      typedef _Pointer pointer;
+
+      typedef _Reference reference;
+    };
+# 149 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+  template<typename _Iterator>
+    struct iterator_traits;
+
+
+
+
+  template<typename _Iterator, typename = __void_t<>>
+    struct __iterator_traits { };
+
+
+
+  template<typename _Iterator>
+    struct __iterator_traits<_Iterator,
+        __void_t<typename _Iterator::iterator_category,
+          typename _Iterator::value_type,
+          typename _Iterator::difference_type,
+          typename _Iterator::pointer,
+          typename _Iterator::reference>>
+    {
+      typedef typename _Iterator::iterator_category iterator_category;
+      typedef typename _Iterator::value_type value_type;
+      typedef typename _Iterator::difference_type difference_type;
+      typedef typename _Iterator::pointer pointer;
+      typedef typename _Iterator::reference reference;
+    };
+
+
+  template<typename _Iterator>
+    struct iterator_traits
+    : public __iterator_traits<_Iterator> { };
+# 209 "/usr/include/c++/13/bits/stl_iterator_base_types.h" 3
+  template<typename _Tp>
+    struct iterator_traits<_Tp*>
+    {
+      typedef random_access_iterator_tag iterator_category;
+      typedef _Tp value_type;
+      typedef ptrdiff_t difference_type;
+      typedef _Tp* pointer;
+      typedef _Tp& reference;
+    };
+
+
+  template<typename _Tp>
+    struct iterator_traits<const _Tp*>
+    {
+      typedef random_access_iterator_tag iterator_category;
+      typedef _Tp value_type;
+      typedef ptrdiff_t difference_type;
+      typedef const _Tp* pointer;
+      typedef const _Tp& reference;
+    };
+
+
+
+
+
+
+  template<typename _Iter>
+    __attribute__((__always_inline__))
+    inline constexpr
+    typename iterator_traits<_Iter>::iterator_category
+    __iterator_category(const _Iter&)
+    { return typename iterator_traits<_Iter>::iterator_category(); }
+
+
+
+
+  template<typename _Iter>
+    using __iter_category_t
+      = typename iterator_traits<_Iter>::iterator_category;
+
+  template<typename _InIter>
+    using _RequireInputIter =
+      __enable_if_t<is_convertible<__iter_category_t<_InIter>,
+       input_iterator_tag>::value>;
+
+  template<typename _It,
+    typename _Cat = __iter_category_t<_It>>
+    struct __is_random_access_iter
+      : is_base_of<random_access_iterator_tag, _Cat>
+    {
+      typedef is_base_of<random_access_iterator_tag, _Cat> _Base;
+      enum { __value = _Base::value };
+    };
+
+
+
+
+
+
+
+
+}
+# 66 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+# 1 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 1 3
+# 62 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 3
+       
+# 63 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 3
+
+# 1 "/usr/include/c++/13/bits/concept_check.h" 1 3
+# 33 "/usr/include/c++/13/bits/concept_check.h" 3
+       
+# 34 "/usr/include/c++/13/bits/concept_check.h" 3
+# 65 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 2 3
+# 1 "/usr/include/c++/13/debug/assertions.h" 1 3
+# 66 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 2 3
+
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+  template <typename> struct _List_iterator;
+  template <typename> struct _List_const_iterator;
+
+
+  template<typename _InputIterator>
+    inline constexpr
+    typename iterator_traits<_InputIterator>::difference_type
+    __distance(_InputIterator __first, _InputIterator __last,
+               input_iterator_tag)
+    {
+
+     
+
+      typename iterator_traits<_InputIterator>::difference_type __n = 0;
+      while (__first != __last)
+ {
+   ++__first;
+   ++__n;
+ }
+      return __n;
+    }
+
+  template<typename _RandomAccessIterator>
+    __attribute__((__always_inline__))
+    inline constexpr
+    typename iterator_traits<_RandomAccessIterator>::difference_type
+    __distance(_RandomAccessIterator __first, _RandomAccessIterator __last,
+               random_access_iterator_tag)
+    {
+
+     
+
+      return __last - __first;
+    }
+
+
+
+  template<typename _Tp>
+    ptrdiff_t
+    __distance(std::_List_iterator<_Tp>,
+        std::_List_iterator<_Tp>,
+        input_iterator_tag);
+
+  template<typename _Tp>
+    ptrdiff_t
+    __distance(std::_List_const_iterator<_Tp>,
+        std::_List_const_iterator<_Tp>,
+        input_iterator_tag);
+
+
+
+
+  template<typename _OutputIterator>
+    void
+    __distance(_OutputIterator, _OutputIterator, output_iterator_tag) = delete;
+# 144 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 3
+  template<typename _InputIterator>
+    [[__nodiscard__]] __attribute__((__always_inline__))
+    inline constexpr
+    typename iterator_traits<_InputIterator>::difference_type
+    distance(_InputIterator __first, _InputIterator __last)
+    {
+
+      return std::__distance(__first, __last,
+        std::__iterator_category(__first));
+    }
+
+  template<typename _InputIterator, typename _Distance>
+    inline constexpr void
+    __advance(_InputIterator& __i, _Distance __n, input_iterator_tag)
+    {
+
+     
+      do { if (std::__is_constant_evaluated() && !bool(__n >= 0)) __builtin_unreachable(); } while (false);
+      while (__n--)
+ ++__i;
+    }
+
+  template<typename _BidirectionalIterator, typename _Distance>
+    inline constexpr void
+    __advance(_BidirectionalIterator& __i, _Distance __n,
+       bidirectional_iterator_tag)
+    {
+
+     
+
+      if (__n > 0)
+        while (__n--)
+   ++__i;
+      else
+        while (__n++)
+   --__i;
+    }
+
+  template<typename _RandomAccessIterator, typename _Distance>
+    inline constexpr void
+    __advance(_RandomAccessIterator& __i, _Distance __n,
+              random_access_iterator_tag)
+    {
+
+     
+
+      if (__builtin_constant_p(__n) && __n == 1)
+ ++__i;
+      else if (__builtin_constant_p(__n) && __n == -1)
+ --__i;
+      else
+ __i += __n;
+    }
+
+
+
+  template<typename _OutputIterator, typename _Distance>
+    void
+    __advance(_OutputIterator&, _Distance, output_iterator_tag) = delete;
+# 217 "/usr/include/c++/13/bits/stl_iterator_base_funcs.h" 3
+  template<typename _InputIterator, typename _Distance>
+    __attribute__((__always_inline__))
+    inline constexpr void
+    advance(_InputIterator& __i, _Distance __n)
+    {
+
+      typename iterator_traits<_InputIterator>::difference_type __d = __n;
+      std::__advance(__i, __d, std::__iterator_category(__i));
+    }
+
+
+
+  template<typename _InputIterator>
+    [[__nodiscard__]] [[__gnu__::__always_inline__]]
+    inline constexpr _InputIterator
+    next(_InputIterator __x, typename
+  iterator_traits<_InputIterator>::difference_type __n = 1)
+    {
+
+     
+      std::advance(__x, __n);
+      return __x;
+    }
+
+  template<typename _BidirectionalIterator>
+    [[__nodiscard__]] [[__gnu__::__always_inline__]]
+    inline constexpr _BidirectionalIterator
+    prev(_BidirectionalIterator __x, typename
+  iterator_traits<_BidirectionalIterator>::difference_type __n = 1)
+    {
+
+     
+
+      std::advance(__x, -__n);
+      return __x;
+    }
+
+
+
+
+}
+# 67 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+# 1 "/usr/include/c++/13/bits/stl_iterator.h" 1 3
+# 67 "/usr/include/c++/13/bits/stl_iterator.h" 3
+# 1 "/usr/include/c++/13/bits/ptr_traits.h" 1 3
+# 49 "/usr/include/c++/13/bits/ptr_traits.h" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+  class __undefined;
+
+
+
+  template<typename _Tp>
+    struct __get_first_arg
+    { using type = __undefined; };
+
+  template<template<typename, typename...> class _SomeTemplate, typename _Tp,
+           typename... _Types>
+    struct __get_first_arg<_SomeTemplate<_Tp, _Types...>>
+    { using type = _Tp; };
+
+
+
+  template<typename _Tp, typename _Up>
+    struct __replace_first_arg
+    { };
+
+  template<template<typename, typename...> class _SomeTemplate, typename _Up,
+           typename _Tp, typename... _Types>
+    struct __replace_first_arg<_SomeTemplate<_Tp, _Types...>, _Up>
+    { using type = _SomeTemplate<_Up, _Types...>; };
+
+
+  template<typename _Ptr, typename = void>
+    struct __ptr_traits_elem : __get_first_arg<_Ptr>
+    { };
+
+
+
+
+
+
+
+  template<typename _Ptr>
+    struct __ptr_traits_elem<_Ptr, __void_t<typename _Ptr::element_type>>
+    { using type = typename _Ptr::element_type; };
+
+
+  template<typename _Ptr>
+    using __ptr_traits_elem_t = typename __ptr_traits_elem<_Ptr>::type;
+
+
+
+
+  template<typename _Ptr, typename _Elt, bool = is_void<_Elt>::value>
+    struct __ptr_traits_ptr_to
+    {
+      using pointer = _Ptr;
+      using element_type = _Elt;
+
+
+
+
+
+
+
+      static pointer
+      pointer_to(element_type& __r)
+
+
+
+
+
+      { return pointer::pointer_to(__r); }
+    };
+
+
+  template<typename _Ptr, typename _Elt>
+    struct __ptr_traits_ptr_to<_Ptr, _Elt, true>
+    { };
+
+
+  template<typename _Tp>
+    struct __ptr_traits_ptr_to<_Tp*, _Tp, false>
+    {
+      using pointer = _Tp*;
+      using element_type = _Tp;
+
+
+
+
+
+
+      static pointer
+      pointer_to(element_type& __r) noexcept
+      { return std::addressof(__r); }
+    };
+
+  template<typename _Ptr, typename _Elt>
+    struct __ptr_traits_impl : __ptr_traits_ptr_to<_Ptr, _Elt>
+    {
+    private:
+      template<typename _Tp>
+ using __diff_t = typename _Tp::difference_type;
+
+      template<typename _Tp, typename _Up>
+ using __rebind = __type_identity<typename _Tp::template rebind<_Up>>;
+
+    public:
+
+      using pointer = _Ptr;
+
+
+      using element_type = _Elt;
+
+
+      using difference_type = __detected_or_t<ptrdiff_t, __diff_t, _Ptr>;
+
+
+      template<typename _Up>
+ using rebind = typename __detected_or_t<__replace_first_arg<_Ptr, _Up>,
+      __rebind, _Ptr, _Up>::type;
+    };
+
+
+
+  template<typename _Ptr>
+    struct __ptr_traits_impl<_Ptr, __undefined>
+    { };
+
+
+
+
+
+
+
+  template<typename _Ptr>
+    struct pointer_traits : __ptr_traits_impl<_Ptr, __ptr_traits_elem_t<_Ptr>>
+    { };
+
+
+
+
+
+
+
+  template<typename _Tp>
+    struct pointer_traits<_Tp*> : __ptr_traits_ptr_to<_Tp*, _Tp>
+    {
+
+      typedef _Tp* pointer;
+
+      typedef _Tp element_type;
+
+      typedef ptrdiff_t difference_type;
+
+      template<typename _Up> using rebind = _Up*;
+    };
+
+
+  template<typename _Ptr, typename _Tp>
+    using __ptr_rebind = typename pointer_traits<_Ptr>::template rebind<_Tp>;
+
+  template<typename _Tp>
+    constexpr _Tp*
+    __to_address(_Tp* __ptr) noexcept
+    {
+      static_assert(!std::is_function<_Tp>::value, "not a function pointer");
+      return __ptr;
+    }
+
+
+  template<typename _Ptr>
+    constexpr typename std::pointer_traits<_Ptr>::element_type*
+    __to_address(const _Ptr& __ptr)
+    { return std::__to_address(__ptr.operator->()); }
+# 266 "/usr/include/c++/13/bits/ptr_traits.h" 3
+
+}
+# 68 "/usr/include/c++/13/bits/stl_iterator.h" 2 3
+# 88 "/usr/include/c++/13/bits/stl_iterator.h" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 113 "/usr/include/c++/13/bits/stl_iterator.h" 3
+ 
+# 113 "/usr/include/c++/13/bits/stl_iterator.h" 3
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+# 135 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+    class reverse_iterator
+    : public iterator<typename iterator_traits<_Iterator>::iterator_category,
+        typename iterator_traits<_Iterator>::value_type,
+        typename iterator_traits<_Iterator>::difference_type,
+        typename iterator_traits<_Iterator>::pointer,
+                      typename iterator_traits<_Iterator>::reference>
+    {
+      template<typename _Iter>
+ friend class reverse_iterator;
+# 154 "/usr/include/c++/13/bits/stl_iterator.h" 3
+    protected:
+      _Iterator current;
+
+      typedef iterator_traits<_Iterator> __traits_type;
+
+    public:
+      typedef _Iterator iterator_type;
+      typedef typename __traits_type::pointer pointer;
+
+      typedef typename __traits_type::difference_type difference_type;
+      typedef typename __traits_type::reference reference;
+# 185 "/usr/include/c++/13/bits/stl_iterator.h" 3
+      constexpr
+      reverse_iterator()
+      noexcept(noexcept(_Iterator()))
+      : current()
+      { }
+
+
+
+
+      explicit constexpr
+      reverse_iterator(iterator_type __x)
+      noexcept(noexcept(_Iterator(__x)))
+      : current(__x)
+      { }
+
+
+
+
+      constexpr
+      reverse_iterator(const reverse_iterator& __x)
+      noexcept(noexcept(_Iterator(__x.current)))
+      : current(__x.current)
+      { }
+
+
+      reverse_iterator& operator=(const reverse_iterator&) = default;
+
+
+
+
+
+
+      template<typename _Iter>
+
+
+
+ constexpr
+        reverse_iterator(const reverse_iterator<_Iter>& __x)
+ noexcept(noexcept(_Iterator(__x.current)))
+ : current(__x.current)
+ { }
+
+
+      template<typename _Iter>
+
+
+
+
+ constexpr
+ reverse_iterator&
+ operator=(const reverse_iterator<_Iter>& __x)
+ noexcept(noexcept(current = __x.current))
+ {
+   current = __x.current;
+   return *this;
+ }
+
+
+
+
+
+      [[__nodiscard__]]
+      constexpr iterator_type
+      base() const
+      noexcept(noexcept(_Iterator(current)))
+      { return current; }
+# 262 "/usr/include/c++/13/bits/stl_iterator.h" 3
+      [[__nodiscard__]]
+      constexpr reference
+      operator*() const
+      {
+ _Iterator __tmp = current;
+ return *--__tmp;
+      }
+
+
+
+
+
+
+      [[__nodiscard__]]
+      constexpr pointer
+      operator->() const
+
+
+
+
+      {
+
+
+ _Iterator __tmp = current;
+ --__tmp;
+ return _S_to_pointer(__tmp);
+      }
+
+
+
+
+
+
+      constexpr reverse_iterator&
+      operator++()
+      {
+ --current;
+ return *this;
+      }
+
+
+
+
+
+
+      constexpr reverse_iterator
+      operator++(int)
+      {
+ reverse_iterator __tmp = *this;
+ --current;
+ return __tmp;
+      }
+
+
+
+
+
+
+      constexpr reverse_iterator&
+      operator--()
+      {
+ ++current;
+ return *this;
+      }
+
+
+
+
+
+
+      constexpr reverse_iterator
+      operator--(int)
+      {
+ reverse_iterator __tmp = *this;
+ ++current;
+ return __tmp;
+      }
+
+
+
+
+
+
+      [[__nodiscard__]]
+      constexpr reverse_iterator
+      operator+(difference_type __n) const
+      { return reverse_iterator(current - __n); }
+
+
+
+
+
+
+
+      constexpr reverse_iterator&
+      operator+=(difference_type __n)
+      {
+ current -= __n;
+ return *this;
+      }
+
+
+
+
+
+
+      [[__nodiscard__]]
+      constexpr reverse_iterator
+      operator-(difference_type __n) const
+      { return reverse_iterator(current + __n); }
+
+
+
+
+
+
+
+      constexpr reverse_iterator&
+      operator-=(difference_type __n)
+      {
+ current += __n;
+ return *this;
+      }
+
+
+
+
+
+
+      [[__nodiscard__]]
+      constexpr reference
+      operator[](difference_type __n) const
+      { return *(*this + __n); }
+# 422 "/usr/include/c++/13/bits/stl_iterator.h" 3
+    private:
+      template<typename _Tp>
+ static constexpr _Tp*
+ _S_to_pointer(_Tp* __p)
+        { return __p; }
+
+      template<typename _Tp>
+ static constexpr pointer
+ _S_to_pointer(_Tp __t)
+        { return __t.operator->(); }
+    };
+# 445 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator==(const reverse_iterator<_Iterator>& __x,
+        const reverse_iterator<_Iterator>& __y)
+    { return __x.base() == __y.base(); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<(const reverse_iterator<_Iterator>& __x,
+       const reverse_iterator<_Iterator>& __y)
+    { return __y.base() < __x.base(); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator!=(const reverse_iterator<_Iterator>& __x,
+        const reverse_iterator<_Iterator>& __y)
+    { return !(__x == __y); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>(const reverse_iterator<_Iterator>& __x,
+       const reverse_iterator<_Iterator>& __y)
+    { return __y < __x; }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<=(const reverse_iterator<_Iterator>& __x,
+        const reverse_iterator<_Iterator>& __y)
+    { return !(__y < __x); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>=(const reverse_iterator<_Iterator>& __x,
+        const reverse_iterator<_Iterator>& __y)
+    { return !(__x < __y); }
+
+
+
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator==(const reverse_iterator<_IteratorL>& __x,
+        const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() == __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<(const reverse_iterator<_IteratorL>& __x,
+       const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() > __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator!=(const reverse_iterator<_IteratorL>& __x,
+        const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() != __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>(const reverse_iterator<_IteratorL>& __x,
+       const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() < __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    inline constexpr bool
+    operator<=(const reverse_iterator<_IteratorL>& __x,
+        const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() >= __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>=(const reverse_iterator<_IteratorL>& __x,
+        const reverse_iterator<_IteratorR>& __y)
+    { return __x.base() <= __y.base(); }
+# 622 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr auto
+    operator-(const reverse_iterator<_IteratorL>& __x,
+       const reverse_iterator<_IteratorR>& __y)
+    -> decltype(__y.base() - __x.base())
+    { return __y.base() - __x.base(); }
+
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr reverse_iterator<_Iterator>
+    operator+(typename reverse_iterator<_Iterator>::difference_type __n,
+       const reverse_iterator<_Iterator>& __x)
+    { return reverse_iterator<_Iterator>(__x.base() - __n); }
+
+
+
+  template<typename _Iterator>
+    inline constexpr reverse_iterator<_Iterator>
+    __make_reverse_iterator(_Iterator __i)
+    { return reverse_iterator<_Iterator>(__i); }
+
+
+
+
+
+
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr reverse_iterator<_Iterator>
+    make_reverse_iterator(_Iterator __i)
+    { return reverse_iterator<_Iterator>(__i); }
+# 666 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+   
+    auto
+    __niter_base(reverse_iterator<_Iterator> __it)
+    -> decltype(__make_reverse_iterator(__niter_base(__it.base())))
+    { return __make_reverse_iterator(__niter_base(__it.base())); }
+
+  template<typename _Iterator>
+    struct __is_move_iterator<reverse_iterator<_Iterator> >
+      : __is_move_iterator<_Iterator>
+    { };
+
+  template<typename _Iterator>
+   
+    auto
+    __miter_base(reverse_iterator<_Iterator> __it)
+    -> decltype(__make_reverse_iterator(__miter_base(__it.base())))
+    { return __make_reverse_iterator(__miter_base(__it.base())); }
+# 697 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    class back_insert_iterator
+    : public iterator<output_iterator_tag, void, void, void, void>
+    {
+    protected:
+      _Container* container;
+
+    public:
+
+      typedef _Container container_type;
+
+
+
+
+
+      explicit
+      back_insert_iterator(_Container& __x)
+      : container(std::__addressof(__x)) { }
+# 735 "/usr/include/c++/13/bits/stl_iterator.h" 3
+     
+      back_insert_iterator&
+      operator=(const typename _Container::value_type& __value)
+      {
+ container->push_back(__value);
+ return *this;
+      }
+
+     
+      back_insert_iterator&
+      operator=(typename _Container::value_type&& __value)
+      {
+ container->push_back(std::move(__value));
+ return *this;
+      }
+
+
+
+      [[__nodiscard__]]
+      back_insert_iterator&
+      operator*()
+      { return *this; }
+
+
+     
+      back_insert_iterator&
+      operator++()
+      { return *this; }
+
+
+     
+      back_insert_iterator
+      operator++(int)
+      { return *this; }
+    };
+# 782 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    [[__nodiscard__]]
+    inline back_insert_iterator<_Container>
+    back_inserter(_Container& __x)
+    { return back_insert_iterator<_Container>(__x); }
+# 798 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    class front_insert_iterator
+    : public iterator<output_iterator_tag, void, void, void, void>
+    {
+    protected:
+      _Container* container;
+
+    public:
+
+      typedef _Container container_type;
+
+
+
+
+
+      explicit
+      front_insert_iterator(_Container& __x)
+      : container(std::__addressof(__x)) { }
+# 836 "/usr/include/c++/13/bits/stl_iterator.h" 3
+     
+      front_insert_iterator&
+      operator=(const typename _Container::value_type& __value)
+      {
+ container->push_front(__value);
+ return *this;
+      }
+
+     
+      front_insert_iterator&
+      operator=(typename _Container::value_type&& __value)
+      {
+ container->push_front(std::move(__value));
+ return *this;
+      }
+
+
+
+      [[__nodiscard__]]
+      front_insert_iterator&
+      operator*()
+      { return *this; }
+
+
+     
+      front_insert_iterator&
+      operator++()
+      { return *this; }
+
+
+     
+      front_insert_iterator
+      operator++(int)
+      { return *this; }
+    };
+# 883 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    [[__nodiscard__]]
+    inline front_insert_iterator<_Container>
+    front_inserter(_Container& __x)
+    { return front_insert_iterator<_Container>(__x); }
+# 903 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    class insert_iterator
+    : public iterator<output_iterator_tag, void, void, void, void>
+    {
+
+
+
+      typedef typename _Container::iterator _Iter;
+
+    protected:
+      _Container* container;
+      _Iter iter;
+
+    public:
+
+      typedef _Container container_type;
+# 928 "/usr/include/c++/13/bits/stl_iterator.h" 3
+     
+      insert_iterator(_Container& __x, _Iter __i)
+      : container(std::__addressof(__x)), iter(__i) {}
+# 964 "/usr/include/c++/13/bits/stl_iterator.h" 3
+     
+      insert_iterator&
+      operator=(const typename _Container::value_type& __value)
+      {
+ iter = container->insert(iter, __value);
+ ++iter;
+ return *this;
+      }
+
+     
+      insert_iterator&
+      operator=(typename _Container::value_type&& __value)
+      {
+ iter = container->insert(iter, std::move(__value));
+ ++iter;
+ return *this;
+      }
+
+
+
+      [[__nodiscard__]]
+      insert_iterator&
+      operator*()
+      { return *this; }
+
+
+     
+      insert_iterator&
+      operator++()
+      { return *this; }
+
+
+     
+      insert_iterator&
+      operator++(int)
+      { return *this; }
+    };
+
+#pragma GCC diagnostic pop
+# 1023 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Container>
+    [[__nodiscard__]]
+    inline insert_iterator<_Container>
+    inserter(_Container& __x, typename _Container::iterator __i)
+    { return insert_iterator<_Container>(__x, __i); }
+
+
+
+
+
+}
+
+namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
+{
+
+# 1046 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator, typename _Container>
+    class __normal_iterator
+    {
+    protected:
+      _Iterator _M_current;
+
+      typedef std::iterator_traits<_Iterator> __traits_type;
+
+
+      template<typename _Iter>
+ using __convertible_from
+   = std::__enable_if_t<std::is_convertible<_Iter, _Iterator>::value>;
+
+
+    public:
+      typedef _Iterator iterator_type;
+      typedef typename __traits_type::iterator_category iterator_category;
+      typedef typename __traits_type::value_type value_type;
+      typedef typename __traits_type::difference_type difference_type;
+      typedef typename __traits_type::reference reference;
+      typedef typename __traits_type::pointer pointer;
+
+
+
+
+
+      constexpr __normal_iterator() noexcept
+      : _M_current(_Iterator()) { }
+
+      explicit
+      __normal_iterator(const _Iterator& __i) noexcept
+      : _M_current(__i) { }
+
+
+
+      template<typename _Iter, typename = __convertible_from<_Iter>>
+
+ __normal_iterator(const __normal_iterator<_Iter, _Container>& __i)
+ noexcept
+# 1094 "/usr/include/c++/13/bits/stl_iterator.h" 3
+        : _M_current(__i.base()) { }
+
+
+     
+      reference
+      operator*() const noexcept
+      { return *_M_current; }
+
+     
+      pointer
+      operator->() const noexcept
+      { return _M_current; }
+
+     
+      __normal_iterator&
+      operator++() noexcept
+      {
+ ++_M_current;
+ return *this;
+      }
+
+     
+      __normal_iterator
+      operator++(int) noexcept
+      { return __normal_iterator(_M_current++); }
+
+
+     
+      __normal_iterator&
+      operator--() noexcept
+      {
+ --_M_current;
+ return *this;
+      }
+
+     
+      __normal_iterator
+      operator--(int) noexcept
+      { return __normal_iterator(_M_current--); }
+
+
+     
+      reference
+      operator[](difference_type __n) const noexcept
+      { return _M_current[__n]; }
+
+     
+      __normal_iterator&
+      operator+=(difference_type __n) noexcept
+      { _M_current += __n; return *this; }
+
+     
+      __normal_iterator
+      operator+(difference_type __n) const noexcept
+      { return __normal_iterator(_M_current + __n); }
+
+     
+      __normal_iterator&
+      operator-=(difference_type __n) noexcept
+      { _M_current -= __n; return *this; }
+
+     
+      __normal_iterator
+      operator-(difference_type __n) const noexcept
+      { return __normal_iterator(_M_current - __n); }
+
+     
+      const _Iterator&
+      base() const noexcept
+      { return _M_current; }
+    };
+# 1214 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator==(const __normal_iterator<_IteratorL, _Container>& __lhs,
+        const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() == __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator==(const __normal_iterator<_Iterator, _Container>& __lhs,
+        const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() == __rhs.base(); }
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator!=(const __normal_iterator<_IteratorL, _Container>& __lhs,
+        const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() != __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator!=(const __normal_iterator<_Iterator, _Container>& __lhs,
+        const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() != __rhs.base(); }
+
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator<(const __normal_iterator<_IteratorL, _Container>& __lhs,
+       const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() < __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator<(const __normal_iterator<_Iterator, _Container>& __lhs,
+       const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() < __rhs.base(); }
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator>(const __normal_iterator<_IteratorL, _Container>& __lhs,
+       const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() > __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator>(const __normal_iterator<_Iterator, _Container>& __lhs,
+       const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() > __rhs.base(); }
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator<=(const __normal_iterator<_IteratorL, _Container>& __lhs,
+        const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() <= __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator<=(const __normal_iterator<_Iterator, _Container>& __lhs,
+        const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() <= __rhs.base(); }
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator>=(const __normal_iterator<_IteratorL, _Container>& __lhs,
+        const __normal_iterator<_IteratorR, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() >= __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline bool
+    operator>=(const __normal_iterator<_Iterator, _Container>& __lhs,
+        const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() >= __rhs.base(); }
+
+
+
+
+
+
+  template<typename _IteratorL, typename _IteratorR, typename _Container>
+
+
+    [[__nodiscard__]]
+    inline auto
+    operator-(const __normal_iterator<_IteratorL, _Container>& __lhs,
+       const __normal_iterator<_IteratorR, _Container>& __rhs) noexcept
+    -> decltype(__lhs.base() - __rhs.base())
+
+
+
+
+
+    { return __lhs.base() - __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline typename __normal_iterator<_Iterator, _Container>::difference_type
+    operator-(const __normal_iterator<_Iterator, _Container>& __lhs,
+       const __normal_iterator<_Iterator, _Container>& __rhs)
+    noexcept
+    { return __lhs.base() - __rhs.base(); }
+
+  template<typename _Iterator, typename _Container>
+    [[__nodiscard__]]
+    inline __normal_iterator<_Iterator, _Container>
+    operator+(typename __normal_iterator<_Iterator, _Container>::difference_type
+       __n, const __normal_iterator<_Iterator, _Container>& __i)
+    noexcept
+    { return __normal_iterator<_Iterator, _Container>(__i.base() + __n); }
+
+
+}
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  template<typename _Iterator, typename _Container>
+   
+    _Iterator
+    __niter_base(__gnu_cxx::__normal_iterator<_Iterator, _Container> __it)
+    noexcept(std::is_nothrow_copy_constructible<_Iterator>::value)
+    { return __it.base(); }
+
+
+
+
+
+
+  template<typename _Iterator, typename _Container>
+    constexpr auto
+    __to_address(const __gnu_cxx::__normal_iterator<_Iterator,
+          _Container>& __it) noexcept
+    -> decltype(std::__to_address(__it.base()))
+    { return std::__to_address(__it.base()); }
+# 1421 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  namespace __detail
+  {
+# 1437 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  }
+# 1448 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+    class move_iterator
+
+
+
+    {
+      _Iterator _M_current;
+
+      using __traits_type = iterator_traits<_Iterator>;
+
+      using __base_ref = typename __traits_type::reference;
+
+
+      template<typename _Iter2>
+ friend class move_iterator;
+# 1487 "/usr/include/c++/13/bits/stl_iterator.h" 3
+    public:
+      using iterator_type = _Iterator;
+# 1501 "/usr/include/c++/13/bits/stl_iterator.h" 3
+      typedef typename __traits_type::iterator_category iterator_category;
+      typedef typename __traits_type::value_type value_type;
+      typedef typename __traits_type::difference_type difference_type;
+
+      typedef _Iterator pointer;
+
+
+      using reference
+ = __conditional_t<is_reference<__base_ref>::value,
+     typename remove_reference<__base_ref>::type&&,
+     __base_ref>;
+
+
+      constexpr
+      move_iterator()
+      : _M_current() { }
+
+      explicit constexpr
+      move_iterator(iterator_type __i)
+      : _M_current(std::move(__i)) { }
+
+      template<typename _Iter>
+
+
+
+ constexpr
+ move_iterator(const move_iterator<_Iter>& __i)
+ : _M_current(__i._M_current) { }
+
+      template<typename _Iter>
+
+
+
+
+ constexpr
+ move_iterator& operator=(const move_iterator<_Iter>& __i)
+ {
+   _M_current = __i._M_current;
+   return *this;
+ }
+
+
+      [[__nodiscard__]]
+      constexpr iterator_type
+      base() const
+      { return _M_current; }
+# 1559 "/usr/include/c++/13/bits/stl_iterator.h" 3
+      [[__nodiscard__]]
+      constexpr reference
+      operator*() const
+
+
+
+      { return static_cast<reference>(*_M_current); }
+
+
+      [[__nodiscard__]]
+      constexpr pointer
+      operator->() const
+      { return _M_current; }
+
+      constexpr move_iterator&
+      operator++()
+      {
+ ++_M_current;
+ return *this;
+      }
+
+      constexpr move_iterator
+      operator++(int)
+      {
+ move_iterator __tmp = *this;
+ ++_M_current;
+ return __tmp;
+      }
+
+
+
+
+
+
+
+      constexpr move_iterator&
+      operator--()
+      {
+ --_M_current;
+ return *this;
+      }
+
+      constexpr move_iterator
+      operator--(int)
+      {
+ move_iterator __tmp = *this;
+ --_M_current;
+ return __tmp;
+      }
+
+      [[__nodiscard__]]
+      constexpr move_iterator
+      operator+(difference_type __n) const
+      { return move_iterator(_M_current + __n); }
+
+      constexpr move_iterator&
+      operator+=(difference_type __n)
+      {
+ _M_current += __n;
+ return *this;
+      }
+
+      [[__nodiscard__]]
+      constexpr move_iterator
+      operator-(difference_type __n) const
+      { return move_iterator(_M_current - __n); }
+
+      constexpr move_iterator&
+      operator-=(difference_type __n)
+      {
+ _M_current -= __n;
+ return *this;
+      }
+
+      [[__nodiscard__]]
+      constexpr reference
+      operator[](difference_type __n) const
+
+
+
+      { return std::move(_M_current[__n]); }
+# 1673 "/usr/include/c++/13/bits/stl_iterator.h" 3
+    };
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator==(const move_iterator<_IteratorL>& __x,
+        const move_iterator<_IteratorR>& __y)
+
+
+
+    { return __x.base() == __y.base(); }
+# 1694 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator!=(const move_iterator<_IteratorL>& __x,
+        const move_iterator<_IteratorR>& __y)
+    { return !(__x == __y); }
+
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<(const move_iterator<_IteratorL>& __x,
+       const move_iterator<_IteratorR>& __y)
+
+
+
+    { return __x.base() < __y.base(); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<=(const move_iterator<_IteratorL>& __x,
+        const move_iterator<_IteratorR>& __y)
+
+
+
+    { return !(__y < __x); }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>(const move_iterator<_IteratorL>& __x,
+       const move_iterator<_IteratorR>& __y)
+
+
+
+    { return __y < __x; }
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>=(const move_iterator<_IteratorL>& __x,
+        const move_iterator<_IteratorR>& __y)
+
+
+
+    { return !(__x < __y); }
+
+
+
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator==(const move_iterator<_Iterator>& __x,
+        const move_iterator<_Iterator>& __y)
+    { return __x.base() == __y.base(); }
+# 1760 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator!=(const move_iterator<_Iterator>& __x,
+        const move_iterator<_Iterator>& __y)
+    { return !(__x == __y); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<(const move_iterator<_Iterator>& __x,
+       const move_iterator<_Iterator>& __y)
+    { return __x.base() < __y.base(); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator<=(const move_iterator<_Iterator>& __x,
+        const move_iterator<_Iterator>& __y)
+    { return !(__y < __x); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>(const move_iterator<_Iterator>& __x,
+       const move_iterator<_Iterator>& __y)
+    { return __y < __x; }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr bool
+    operator>=(const move_iterator<_Iterator>& __x,
+        const move_iterator<_Iterator>& __y)
+    { return !(__x < __y); }
+
+
+
+  template<typename _IteratorL, typename _IteratorR>
+    [[__nodiscard__]]
+    inline constexpr auto
+    operator-(const move_iterator<_IteratorL>& __x,
+       const move_iterator<_IteratorR>& __y)
+    -> decltype(__x.base() - __y.base())
+    { return __x.base() - __y.base(); }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr move_iterator<_Iterator>
+    operator+(typename move_iterator<_Iterator>::difference_type __n,
+       const move_iterator<_Iterator>& __x)
+    { return __x + __n; }
+
+  template<typename _Iterator>
+    [[__nodiscard__]]
+    inline constexpr move_iterator<_Iterator>
+    make_move_iterator(_Iterator __i)
+    { return move_iterator<_Iterator>(std::move(__i)); }
+
+  template<typename _Iterator, typename _ReturnType
+    = __conditional_t<__move_if_noexcept_cond
+      <typename iterator_traits<_Iterator>::value_type>::value,
+  _Iterator, move_iterator<_Iterator>>>
+    inline constexpr _ReturnType
+    __make_move_if_noexcept_iterator(_Iterator __i)
+    { return _ReturnType(__i); }
+
+
+
+  template<typename _Tp, typename _ReturnType
+    = __conditional_t<__move_if_noexcept_cond<_Tp>::value,
+        const _Tp*, move_iterator<_Tp*>>>
+    inline constexpr _ReturnType
+    __make_move_if_noexcept_iterator(_Tp* __i)
+    { return _ReturnType(__i); }
+# 2951 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _Iterator>
+   
+    auto
+    __niter_base(move_iterator<_Iterator> __it)
+    -> decltype(make_move_iterator(__niter_base(__it.base())))
+    { return make_move_iterator(__niter_base(__it.base())); }
+
+  template<typename _Iterator>
+    struct __is_move_iterator<move_iterator<_Iterator> >
+    {
+      enum { __value = 1 };
+      typedef __true_type __type;
+    };
+
+  template<typename _Iterator>
+   
+    auto
+    __miter_base(move_iterator<_Iterator> __it)
+    -> decltype(__miter_base(__it.base()))
+    { return __miter_base(__it.base()); }
+# 2983 "/usr/include/c++/13/bits/stl_iterator.h" 3
+  template<typename _InputIterator>
+    using __iter_key_t = remove_const_t<
+      typename iterator_traits<_InputIterator>::value_type::first_type>;
+
+  template<typename _InputIterator>
+    using __iter_val_t
+      = typename iterator_traits<_InputIterator>::value_type::second_type;
+
+  template<typename _T1, typename _T2>
+    struct pair;
+
+  template<typename _InputIterator>
+    using __iter_to_alloc_t
+      = pair<const __iter_key_t<_InputIterator>, __iter_val_t<_InputIterator>>;
+
+
+
+}
+# 68 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+
+# 1 "/usr/include/c++/13/debug/debug.h" 1 3
+# 48 "/usr/include/c++/13/debug/debug.h" 3
+namespace std
+{
+  namespace __debug { }
+}
+
+
+
+
+namespace __gnu_debug
+{
+  using namespace std::__debug;
+
+  template<typename _Ite, typename _Seq, typename _Cat>
+    struct _Safe_iterator;
+}
+# 70 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+
+# 1 "/usr/include/c++/13/bits/predefined_ops.h" 1 3
+# 35 "/usr/include/c++/13/bits/predefined_ops.h" 3
+namespace __gnu_cxx
+{
+namespace __ops
+{
+  struct _Iter_less_iter
+  {
+    template<typename _Iterator1, typename _Iterator2>
+      constexpr
+      bool
+      operator()(_Iterator1 __it1, _Iterator2 __it2) const
+      { return *__it1 < *__it2; }
+  };
+
+  constexpr
+  inline _Iter_less_iter
+  __iter_less_iter()
+  { return _Iter_less_iter(); }
+
+  struct _Iter_less_val
+  {
+
+    constexpr _Iter_less_val() = default;
+
+
+
+
+   
+    explicit
+    _Iter_less_val(_Iter_less_iter) { }
+
+    template<typename _Iterator, typename _Value>
+     
+      bool
+      operator()(_Iterator __it, _Value& __val) const
+      { return *__it < __val; }
+  };
+
+ 
+  inline _Iter_less_val
+  __iter_less_val()
+  { return _Iter_less_val(); }
+
+ 
+  inline _Iter_less_val
+  __iter_comp_val(_Iter_less_iter)
+  { return _Iter_less_val(); }
+
+  struct _Val_less_iter
+  {
+
+    constexpr _Val_less_iter() = default;
+
+
+
+
+   
+    explicit
+    _Val_less_iter(_Iter_less_iter) { }
+
+    template<typename _Value, typename _Iterator>
+     
+      bool
+      operator()(_Value& __val, _Iterator __it) const
+      { return __val < *__it; }
+  };
+
+ 
+  inline _Val_less_iter
+  __val_less_iter()
+  { return _Val_less_iter(); }
+
+ 
+  inline _Val_less_iter
+  __val_comp_iter(_Iter_less_iter)
+  { return _Val_less_iter(); }
+
+  struct _Iter_equal_to_iter
+  {
+    template<typename _Iterator1, typename _Iterator2>
+     
+      bool
+      operator()(_Iterator1 __it1, _Iterator2 __it2) const
+      { return *__it1 == *__it2; }
+  };
+
+ 
+  inline _Iter_equal_to_iter
+  __iter_equal_to_iter()
+  { return _Iter_equal_to_iter(); }
+
+  struct _Iter_equal_to_val
+  {
+    template<typename _Iterator, typename _Value>
+     
+      bool
+      operator()(_Iterator __it, _Value& __val) const
+      { return *__it == __val; }
+  };
+
+ 
+  inline _Iter_equal_to_val
+  __iter_equal_to_val()
+  { return _Iter_equal_to_val(); }
+
+ 
+  inline _Iter_equal_to_val
+  __iter_comp_val(_Iter_equal_to_iter)
+  { return _Iter_equal_to_val(); }
+
+  template<typename _Compare>
+    struct _Iter_comp_iter
+    {
+      _Compare _M_comp;
+
+      explicit constexpr
+      _Iter_comp_iter(_Compare __comp)
+ : _M_comp(std::move(__comp))
+      { }
+
+      template<typename _Iterator1, typename _Iterator2>
+        constexpr
+        bool
+        operator()(_Iterator1 __it1, _Iterator2 __it2)
+        { return bool(_M_comp(*__it1, *__it2)); }
+    };
+
+  template<typename _Compare>
+    constexpr
+    inline _Iter_comp_iter<_Compare>
+    __iter_comp_iter(_Compare __comp)
+    { return _Iter_comp_iter<_Compare>(std::move(__comp)); }
+
+  template<typename _Compare>
+    struct _Iter_comp_val
+    {
+      _Compare _M_comp;
+
+     
+      explicit
+      _Iter_comp_val(_Compare __comp)
+ : _M_comp(std::move(__comp))
+      { }
+
+     
+      explicit
+      _Iter_comp_val(const _Iter_comp_iter<_Compare>& __comp)
+ : _M_comp(__comp._M_comp)
+      { }
+
+
+     
+      explicit
+      _Iter_comp_val(_Iter_comp_iter<_Compare>&& __comp)
+ : _M_comp(std::move(__comp._M_comp))
+      { }
+
+
+      template<typename _Iterator, typename _Value>
+
+ bool
+ operator()(_Iterator __it, _Value& __val)
+ { return bool(_M_comp(*__it, __val)); }
+    };
+
+  template<typename _Compare>
+   
+    inline _Iter_comp_val<_Compare>
+    __iter_comp_val(_Compare __comp)
+    { return _Iter_comp_val<_Compare>(std::move(__comp)); }
+
+  template<typename _Compare>
+   
+    inline _Iter_comp_val<_Compare>
+    __iter_comp_val(_Iter_comp_iter<_Compare> __comp)
+    { return _Iter_comp_val<_Compare>(std::move(__comp)); }
+
+  template<typename _Compare>
+    struct _Val_comp_iter
+    {
+      _Compare _M_comp;
+
+     
+      explicit
+      _Val_comp_iter(_Compare __comp)
+ : _M_comp(std::move(__comp))
+      { }
+
+     
+      explicit
+      _Val_comp_iter(const _Iter_comp_iter<_Compare>& __comp)
+ : _M_comp(__comp._M_comp)
+      { }
+
+
+     
+      explicit
+      _Val_comp_iter(_Iter_comp_iter<_Compare>&& __comp)
+ : _M_comp(std::move(__comp._M_comp))
+      { }
+
+
+      template<typename _Value, typename _Iterator>
+
+ bool
+ operator()(_Value& __val, _Iterator __it)
+ { return bool(_M_comp(__val, *__it)); }
+    };
+
+  template<typename _Compare>
+   
+    inline _Val_comp_iter<_Compare>
+    __val_comp_iter(_Compare __comp)
+    { return _Val_comp_iter<_Compare>(std::move(__comp)); }
+
+  template<typename _Compare>
+   
+    inline _Val_comp_iter<_Compare>
+    __val_comp_iter(_Iter_comp_iter<_Compare> __comp)
+    { return _Val_comp_iter<_Compare>(std::move(__comp)); }
+
+  template<typename _Value>
+    struct _Iter_equals_val
+    {
+      _Value& _M_value;
+
+     
+      explicit
+      _Iter_equals_val(_Value& __value)
+ : _M_value(__value)
+      { }
+
+      template<typename _Iterator>
+
+ bool
+ operator()(_Iterator __it)
+ { return *__it == _M_value; }
+    };
+
+  template<typename _Value>
+   
+    inline _Iter_equals_val<_Value>
+    __iter_equals_val(_Value& __val)
+    { return _Iter_equals_val<_Value>(__val); }
+
+  template<typename _Iterator1>
+    struct _Iter_equals_iter
+    {
+      _Iterator1 _M_it1;
+
+     
+      explicit
+      _Iter_equals_iter(_Iterator1 __it1)
+ : _M_it1(__it1)
+      { }
+
+      template<typename _Iterator2>
+
+ bool
+ operator()(_Iterator2 __it2)
+ { return *__it2 == *_M_it1; }
+    };
+
+  template<typename _Iterator>
+   
+    inline _Iter_equals_iter<_Iterator>
+    __iter_comp_iter(_Iter_equal_to_iter, _Iterator __it)
+    { return _Iter_equals_iter<_Iterator>(__it); }
+
+  template<typename _Predicate>
+    struct _Iter_pred
+    {
+      _Predicate _M_pred;
+
+     
+      explicit
+      _Iter_pred(_Predicate __pred)
+ : _M_pred(std::move(__pred))
+      { }
+
+      template<typename _Iterator>
+
+ bool
+ operator()(_Iterator __it)
+ { return bool(_M_pred(*__it)); }
+    };
+
+  template<typename _Predicate>
+   
+    inline _Iter_pred<_Predicate>
+    __pred_iter(_Predicate __pred)
+    { return _Iter_pred<_Predicate>(std::move(__pred)); }
+
+  template<typename _Compare, typename _Value>
+    struct _Iter_comp_to_val
+    {
+      _Compare _M_comp;
+      _Value& _M_value;
+
+     
+      _Iter_comp_to_val(_Compare __comp, _Value& __value)
+ : _M_comp(std::move(__comp)), _M_value(__value)
+      { }
+
+      template<typename _Iterator>
+
+ bool
+ operator()(_Iterator __it)
+ { return bool(_M_comp(*__it, _M_value)); }
+    };
+
+  template<typename _Compare, typename _Value>
+    _Iter_comp_to_val<_Compare, _Value>
+   
+    __iter_comp_val(_Compare __comp, _Value &__val)
+    {
+      return _Iter_comp_to_val<_Compare, _Value>(std::move(__comp), __val);
+    }
+
+  template<typename _Compare, typename _Iterator1>
+    struct _Iter_comp_to_iter
+    {
+      _Compare _M_comp;
+      _Iterator1 _M_it1;
+
+     
+      _Iter_comp_to_iter(_Compare __comp, _Iterator1 __it1)
+ : _M_comp(std::move(__comp)), _M_it1(__it1)
+      { }
+
+      template<typename _Iterator2>
+
+ bool
+ operator()(_Iterator2 __it2)
+ { return bool(_M_comp(*__it2, *_M_it1)); }
+    };
+
+  template<typename _Compare, typename _Iterator>
+   
+    inline _Iter_comp_to_iter<_Compare, _Iterator>
+    __iter_comp_iter(_Iter_comp_iter<_Compare> __comp, _Iterator __it)
+    {
+      return _Iter_comp_to_iter<_Compare, _Iterator>(
+   std::move(__comp._M_comp), __it);
+    }
+
+  template<typename _Predicate>
+    struct _Iter_negate
+    {
+      _Predicate _M_pred;
+
+     
+      explicit
+      _Iter_negate(_Predicate __pred)
+ : _M_pred(std::move(__pred))
+      { }
+
+      template<typename _Iterator>
+
+ bool
+ operator()(_Iterator __it)
+ { return !bool(_M_pred(*__it)); }
+    };
+
+  template<typename _Predicate>
+   
+    inline _Iter_negate<_Predicate>
+    __negate(_Iter_pred<_Predicate> __pred)
+    { return _Iter_negate<_Predicate>(std::move(__pred._M_pred)); }
+
+}
+}
+# 72 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+
+
+
+
+# 1 "/usr/include/c++/13/bit" 1 3
+# 32 "/usr/include/c++/13/bit" 3
+       
+# 33 "/usr/include/c++/13/bit" 3
+# 55 "/usr/include/c++/13/bit" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 149 "/usr/include/c++/13/bit" 3
+  template<typename _Tp>
+    constexpr _Tp
+    __rotl(_Tp __x, int __s) noexcept
+    {
+      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
+      if constexpr ((_Nd & (_Nd - 1)) == 0)
+ {
+
+
+   constexpr unsigned __uNd = _Nd;
+   const unsigned __r = __s;
+   return (__x << (__r % __uNd)) | (__x >> ((-__r) % __uNd));
+ }
+      const int __r = __s % _Nd;
+      if (__r == 0)
+ return __x;
+      else if (__r > 0)
+ return (__x << __r) | (__x >> ((_Nd - __r) % _Nd));
+      else
+ return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd));
+    }
+
+  template<typename _Tp>
+    constexpr _Tp
+    __rotr(_Tp __x, int __s) noexcept
+    {
+      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
+      if constexpr ((_Nd & (_Nd - 1)) == 0)
+ {
+
+
+   constexpr unsigned __uNd = _Nd;
+   const unsigned __r = __s;
+   return (__x >> (__r % __uNd)) | (__x << ((-__r) % __uNd));
+ }
+      const int __r = __s % _Nd;
+      if (__r == 0)
+ return __x;
+      else if (__r > 0)
+ return (__x >> __r) | (__x << ((_Nd - __r) % _Nd));
+      else
+ return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd));
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __countl_zero(_Tp __x) noexcept
+    {
+      using __gnu_cxx::__int_traits;
+      constexpr auto _Nd = __int_traits<_Tp>::__digits;
+
+      if (__x == 0)
+        return _Nd;
+
+      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
+      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
+      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
+
+      if constexpr (_Nd <= _Nd_u)
+ {
+   constexpr int __diff = _Nd_u - _Nd;
+   return __builtin_clz(__x) - __diff;
+ }
+      else if constexpr (_Nd <= _Nd_ul)
+ {
+   constexpr int __diff = _Nd_ul - _Nd;
+   return __builtin_clzl(__x) - __diff;
+ }
+      else if constexpr (_Nd <= _Nd_ull)
+ {
+   constexpr int __diff = _Nd_ull - _Nd;
+   return __builtin_clzll(__x) - __diff;
+ }
+      else
+ {
+   static_assert(_Nd <= (2 * _Nd_ull),
+   "Maximum supported integer size is 128-bit");
+
+   unsigned long long __high = __x >> _Nd_ull;
+   if (__high != 0)
+     {
+       constexpr int __diff = (2 * _Nd_ull) - _Nd;
+       return __builtin_clzll(__high) - __diff;
+     }
+   constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
+   unsigned long long __low = __x & __max_ull;
+   return (_Nd - _Nd_ull) + __builtin_clzll(__low);
+ }
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __countl_one(_Tp __x) noexcept
+    {
+      return std::__countl_zero<_Tp>((_Tp)~__x);
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __countr_zero(_Tp __x) noexcept
+    {
+      using __gnu_cxx::__int_traits;
+      constexpr auto _Nd = __int_traits<_Tp>::__digits;
+
+      if (__x == 0)
+        return _Nd;
+
+      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
+      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
+      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
+
+      if constexpr (_Nd <= _Nd_u)
+ return __builtin_ctz(__x);
+      else if constexpr (_Nd <= _Nd_ul)
+ return __builtin_ctzl(__x);
+      else if constexpr (_Nd <= _Nd_ull)
+ return __builtin_ctzll(__x);
+      else
+ {
+   static_assert(_Nd <= (2 * _Nd_ull),
+   "Maximum supported integer size is 128-bit");
+
+   constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
+   unsigned long long __low = __x & __max_ull;
+   if (__low != 0)
+     return __builtin_ctzll(__low);
+   unsigned long long __high = __x >> _Nd_ull;
+   return __builtin_ctzll(__high) + _Nd_ull;
+ }
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __countr_one(_Tp __x) noexcept
+    {
+      return std::__countr_zero((_Tp)~__x);
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __popcount(_Tp __x) noexcept
+    {
+      using __gnu_cxx::__int_traits;
+      constexpr auto _Nd = __int_traits<_Tp>::__digits;
+
+      constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
+      constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
+      constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
+
+      if constexpr (_Nd <= _Nd_u)
+ return __builtin_popcount(__x);
+      else if constexpr (_Nd <= _Nd_ul)
+ return __builtin_popcountl(__x);
+      else if constexpr (_Nd <= _Nd_ull)
+ return __builtin_popcountll(__x);
+      else
+ {
+   static_assert(_Nd <= (2 * _Nd_ull),
+   "Maximum supported integer size is 128-bit");
+
+   constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
+   unsigned long long __low = __x & __max_ull;
+   unsigned long long __high = __x >> _Nd_ull;
+   return __builtin_popcountll(__low) + __builtin_popcountll(__high);
+ }
+    }
+
+  template<typename _Tp>
+    constexpr bool
+    __has_single_bit(_Tp __x) noexcept
+    { return std::__popcount(__x) == 1; }
+
+  template<typename _Tp>
+    constexpr _Tp
+    __bit_ceil(_Tp __x) noexcept
+    {
+      using __gnu_cxx::__int_traits;
+      constexpr auto _Nd = __int_traits<_Tp>::__digits;
+      if (__x == 0 || __x == 1)
+        return 1;
+      auto __shift_exponent = _Nd - std::__countl_zero((_Tp)(__x - 1u));
+
+
+
+
+      if (!std::__is_constant_evaluated())
+ {
+   do { if (std::__is_constant_evaluated() && !bool(__shift_exponent != __int_traits<_Tp>::__digits)) __builtin_unreachable(); } while (false);
+ }
+
+      using __promoted_type = decltype(__x << 1);
+      if constexpr (!is_same<__promoted_type, _Tp>::value)
+ {
+
+
+
+
+
+   const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
+   __shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
+ }
+      return (_Tp)1u << __shift_exponent;
+    }
+
+  template<typename _Tp>
+    constexpr _Tp
+    __bit_floor(_Tp __x) noexcept
+    {
+      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
+      if (__x == 0)
+        return 0;
+      return (_Tp)1u << (_Nd - std::__countl_zero((_Tp)(__x >> 1)));
+    }
+
+  template<typename _Tp>
+    constexpr int
+    __bit_width(_Tp __x) noexcept
+    {
+      constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
+      return _Nd - std::__countl_zero(__x);
+    }
+# 478 "/usr/include/c++/13/bit" 3
+
+}
+# 77 "/usr/include/c++/13/bits/stl_algobase.h" 2 3
+
+
+
+
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+
+
+  template<typename _Tp, typename _Up>
+    constexpr
+    inline int
+    __memcmp(const _Tp* __first1, const _Up* __first2, size_t __num)
+    {
+
+      static_assert(sizeof(_Tp) == sizeof(_Up), "can be compared with memcmp");
+# 108 "/usr/include/c++/13/bits/stl_algobase.h" 3
+ return __builtin_memcmp(__first1, __first2, sizeof(_Tp) * __num);
+    }
+# 152 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _ForwardIterator1, typename _ForwardIterator2>
+   
+    inline void
+    iter_swap(_ForwardIterator1 __a, _ForwardIterator2 __b)
+    {
+
+     
+
+     
+# 185 "/usr/include/c++/13/bits/stl_algobase.h" 3
+      swap(*__a, *__b);
+
+    }
+# 201 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _ForwardIterator1, typename _ForwardIterator2>
+   
+    _ForwardIterator2
+    swap_ranges(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
+  _ForwardIterator2 __first2)
+    {
+
+     
+
+     
+
+      ;
+
+      for (; __first1 != __last1; ++__first1, (void)++__first2)
+ std::iter_swap(__first1, __first2);
+      return __first2;
+    }
+# 230 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _Tp>
+    constexpr
+    inline const _Tp&
+    min(const _Tp& __a, const _Tp& __b)
+    {
+
+     
+
+      if (__b < __a)
+ return __b;
+      return __a;
+    }
+# 254 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _Tp>
+    constexpr
+    inline const _Tp&
+    max(const _Tp& __a, const _Tp& __b)
+    {
+
+     
+
+      if (__a < __b)
+ return __b;
+      return __a;
+    }
+# 278 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _Tp, typename _Compare>
+    constexpr
+    inline const _Tp&
+    min(const _Tp& __a, const _Tp& __b, _Compare __comp)
+    {
+
+      if (__comp(__b, __a))
+ return __b;
+      return __a;
+    }
+# 300 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _Tp, typename _Compare>
+    constexpr
+    inline const _Tp&
+    max(const _Tp& __a, const _Tp& __b, _Compare __comp)
+    {
+
+      if (__comp(__a, __b))
+ return __b;
+      return __a;
+    }
+
+
+
+  template<typename _Iterator>
+   
+    inline _Iterator
+    __niter_base(_Iterator __it)
+    noexcept(std::is_nothrow_copy_constructible<_Iterator>::value)
+    { return __it; }
+
+  template<typename _Ite, typename _Seq>
+    _Ite
+    __niter_base(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq,
+   std::random_access_iterator_tag>&);
+
+
+
+
+  template<typename _From, typename _To>
+   
+    inline _From
+    __niter_wrap(_From __from, _To __res)
+    { return __from + (__res - std::__niter_base(__from)); }
+
+
+  template<typename _Iterator>
+   
+    inline _Iterator
+    __niter_wrap(const _Iterator&, _Iterator __res)
+    { return __res; }
+
+
+
+
+
+
+
+  template<bool _IsMove, bool _IsSimple, typename _Category>
+    struct __copy_move
+    {
+      template<typename _II, typename _OI>
+
+ static _OI
+ __copy_m(_II __first, _II __last, _OI __result)
+ {
+   for (; __first != __last; ++__result, (void)++__first)
+     *__result = *__first;
+   return __result;
+ }
+    };
+
+
+  template<typename _Category>
+    struct __copy_move<true, false, _Category>
+    {
+      template<typename _II, typename _OI>
+
+ static _OI
+ __copy_m(_II __first, _II __last, _OI __result)
+ {
+   for (; __first != __last; ++__result, (void)++__first)
+     *__result = std::move(*__first);
+   return __result;
+ }
+    };
+
+
+  template<>
+    struct __copy_move<false, false, random_access_iterator_tag>
+    {
+      template<typename _II, typename _OI>
+
+ static _OI
+ __copy_m(_II __first, _II __last, _OI __result)
+ {
+   typedef typename iterator_traits<_II>::difference_type _Distance;
+   for(_Distance __n = __last - __first; __n > 0; --__n)
+     {
+       *__result = *__first;
+       ++__first;
+       ++__result;
+     }
+   return __result;
+ }
+
+      template<typename _Tp, typename _Up>
+ static void
+ __assign_one(_Tp* __to, _Up* __from)
+ { *__to = *__from; }
+    };
+
+
+  template<>
+    struct __copy_move<true, false, random_access_iterator_tag>
+    {
+      template<typename _II, typename _OI>
+
+ static _OI
+ __copy_m(_II __first, _II __last, _OI __result)
+ {
+   typedef typename iterator_traits<_II>::difference_type _Distance;
+   for(_Distance __n = __last - __first; __n > 0; --__n)
+     {
+       *__result = std::move(*__first);
+       ++__first;
+       ++__result;
+     }
+   return __result;
+ }
+
+      template<typename _Tp, typename _Up>
+ static void
+ __assign_one(_Tp* __to, _Up* __from)
+ { *__to = std::move(*__from); }
+    };
+
+
+  template<bool _IsMove>
+    struct __copy_move<_IsMove, true, random_access_iterator_tag>
+    {
+      template<typename _Tp, typename _Up>
+
+ static _Up*
+ __copy_m(_Tp* __first, _Tp* __last, _Up* __result)
+ {
+   const ptrdiff_t _Num = __last - __first;
+   if (__builtin_expect(_Num > 1, true))
+     __builtin_memmove(__result, __first, sizeof(_Tp) * _Num);
+   else if (_Num == 1)
+     std::__copy_move<_IsMove, false, random_access_iterator_tag>::
+       __assign_one(__result, __first);
+   return __result + _Num;
+ }
+    };
+
+
+
+  template<typename _Tp, typename _Ref, typename _Ptr>
+    struct _Deque_iterator;
+
+  struct _Bit_iterator;
+
+
+
+
+
+
+  template<typename _CharT>
+    struct char_traits;
+
+  template<typename _CharT, typename _Traits>
+    class istreambuf_iterator;
+
+  template<typename _CharT, typename _Traits>
+    class ostreambuf_iterator;
+
+  template<bool _IsMove, typename _CharT>
+    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
+      ostreambuf_iterator<_CharT, char_traits<_CharT> > >::__type
+    __copy_move_a2(_CharT*, _CharT*,
+     ostreambuf_iterator<_CharT, char_traits<_CharT> >);
+
+  template<bool _IsMove, typename _CharT>
+    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
+      ostreambuf_iterator<_CharT, char_traits<_CharT> > >::__type
+    __copy_move_a2(const _CharT*, const _CharT*,
+     ostreambuf_iterator<_CharT, char_traits<_CharT> >);
+
+  template<bool _IsMove, typename _CharT>
+    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
+        _CharT*>::__type
+    __copy_move_a2(istreambuf_iterator<_CharT, char_traits<_CharT> >,
+     istreambuf_iterator<_CharT, char_traits<_CharT> >, _CharT*);
+
+  template<bool _IsMove, typename _CharT>
+    typename __gnu_cxx::__enable_if<
+      __is_char<_CharT>::__value,
+      std::_Deque_iterator<_CharT, _CharT&, _CharT*> >::__type
+    __copy_move_a2(
+ istreambuf_iterator<_CharT, char_traits<_CharT> >,
+ istreambuf_iterator<_CharT, char_traits<_CharT> >,
+ std::_Deque_iterator<_CharT, _CharT&, _CharT*>);
+
+
+  template<bool _IsMove, typename _II, typename _OI>
+   
+    inline _OI
+    __copy_move_a2(_II __first, _II __last, _OI __result)
+    {
+      typedef typename iterator_traits<_II>::iterator_category _Category;
+
+
+
+
+
+      return std::__copy_move<_IsMove, __memcpyable<_OI, _II>::__value,
+         _Category>::__copy_m(__first, __last, __result);
+    }
+
+  template<bool _IsMove,
+    typename _Tp, typename _Ref, typename _Ptr, typename _OI>
+    _OI
+    __copy_move_a1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+     std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+     _OI);
+
+  template<bool _IsMove,
+    typename _ITp, typename _IRef, typename _IPtr, typename _OTp>
+    std::_Deque_iterator<_OTp, _OTp&, _OTp*>
+    __copy_move_a1(std::_Deque_iterator<_ITp, _IRef, _IPtr>,
+     std::_Deque_iterator<_ITp, _IRef, _IPtr>,
+     std::_Deque_iterator<_OTp, _OTp&, _OTp*>);
+
+  template<bool _IsMove, typename _II, typename _Tp>
+    typename __gnu_cxx::__enable_if<
+      __is_random_access_iter<_II>::__value,
+      std::_Deque_iterator<_Tp, _Tp&, _Tp*> >::__type
+    __copy_move_a1(_II, _II, std::_Deque_iterator<_Tp, _Tp&, _Tp*>);
+
+  template<bool _IsMove, typename _II, typename _OI>
+   
+    inline _OI
+    __copy_move_a1(_II __first, _II __last, _OI __result)
+    { return std::__copy_move_a2<_IsMove>(__first, __last, __result); }
+
+  template<bool _IsMove, typename _II, typename _OI>
+   
+    inline _OI
+    __copy_move_a(_II __first, _II __last, _OI __result)
+    {
+      return std::__niter_wrap(__result,
+  std::__copy_move_a1<_IsMove>(std::__niter_base(__first),
+          std::__niter_base(__last),
+          std::__niter_base(__result)));
+    }
+
+  template<bool _IsMove,
+    typename _Ite, typename _Seq, typename _Cat, typename _OI>
+    _OI
+    __copy_move_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+    const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+    _OI);
+
+  template<bool _IsMove,
+    typename _II, typename _Ite, typename _Seq, typename _Cat>
+    __gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
+    __copy_move_a(_II, _II,
+    const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&);
+
+  template<bool _IsMove,
+    typename _IIte, typename _ISeq, typename _ICat,
+    typename _OIte, typename _OSeq, typename _OCat>
+    ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>
+    __copy_move_a(const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
+    const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
+    const ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>&);
+
+  template<typename _InputIterator, typename _Size, typename _OutputIterator>
+   
+    _OutputIterator
+    __copy_n_a(_InputIterator __first, _Size __n, _OutputIterator __result,
+        bool)
+    {
+      if (__n > 0)
+ {
+   while (true)
+     {
+       *__result = *__first;
+       ++__result;
+       if (--__n > 0)
+  ++__first;
+       else
+  break;
+     }
+ }
+      return __result;
+    }
+
+
+  template<typename _CharT, typename _Size>
+    typename __gnu_cxx::__enable_if<
+      __is_char<_CharT>::__value, _CharT*>::__type
+    __copy_n_a(istreambuf_iterator<_CharT, char_traits<_CharT> >,
+        _Size, _CharT*, bool);
+
+  template<typename _CharT, typename _Size>
+    typename __gnu_cxx::__enable_if<
+      __is_char<_CharT>::__value,
+      std::_Deque_iterator<_CharT, _CharT&, _CharT*> >::__type
+    __copy_n_a(istreambuf_iterator<_CharT, char_traits<_CharT> >, _Size,
+        std::_Deque_iterator<_CharT, _CharT&, _CharT*>,
+        bool);
+# 621 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II, typename _OI>
+   
+    inline _OI
+    copy(_II __first, _II __last, _OI __result)
+    {
+
+     
+     
+
+      ;
+
+      return std::__copy_move_a<__is_move_iterator<_II>::__value>
+      (std::__miter_base(__first), std::__miter_base(__last), __result);
+    }
+# 654 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II, typename _OI>
+   
+    inline _OI
+    move(_II __first, _II __last, _OI __result)
+    {
+
+     
+     
+
+      ;
+
+      return std::__copy_move_a<true>(std::__miter_base(__first),
+          std::__miter_base(__last), __result);
+    }
+
+
+
+
+
+
+  template<bool _IsMove, bool _IsSimple, typename _Category>
+    struct __copy_move_backward
+    {
+      template<typename _BI1, typename _BI2>
+
+ static _BI2
+ __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
+ {
+   while (__first != __last)
+     *--__result = *--__last;
+   return __result;
+ }
+    };
+
+
+  template<typename _Category>
+    struct __copy_move_backward<true, false, _Category>
+    {
+      template<typename _BI1, typename _BI2>
+
+ static _BI2
+ __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
+ {
+   while (__first != __last)
+     *--__result = std::move(*--__last);
+   return __result;
+ }
+    };
+
+
+  template<>
+    struct __copy_move_backward<false, false, random_access_iterator_tag>
+    {
+      template<typename _BI1, typename _BI2>
+
+ static _BI2
+ __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
+ {
+   typename iterator_traits<_BI1>::difference_type
+     __n = __last - __first;
+   for (; __n > 0; --__n)
+     *--__result = *--__last;
+   return __result;
+ }
+    };
+
+
+  template<>
+    struct __copy_move_backward<true, false, random_access_iterator_tag>
+    {
+      template<typename _BI1, typename _BI2>
+
+ static _BI2
+ __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
+ {
+   typename iterator_traits<_BI1>::difference_type
+     __n = __last - __first;
+   for (; __n > 0; --__n)
+     *--__result = std::move(*--__last);
+   return __result;
+ }
+    };
+
+
+  template<bool _IsMove>
+    struct __copy_move_backward<_IsMove, true, random_access_iterator_tag>
+    {
+      template<typename _Tp, typename _Up>
+
+ static _Up*
+ __copy_move_b(_Tp* __first, _Tp* __last, _Up* __result)
+ {
+   const ptrdiff_t _Num = __last - __first;
+   if (__builtin_expect(_Num > 1, true))
+     __builtin_memmove(__result - _Num, __first, sizeof(_Tp) * _Num);
+   else if (_Num == 1)
+     std::__copy_move<_IsMove, false, random_access_iterator_tag>::
+       __assign_one(__result - 1, __first);
+   return __result - _Num;
+ }
+    };
+
+  template<bool _IsMove, typename _BI1, typename _BI2>
+   
+    inline _BI2
+    __copy_move_backward_a2(_BI1 __first, _BI1 __last, _BI2 __result)
+    {
+      typedef typename iterator_traits<_BI1>::iterator_category _Category;
+
+
+
+
+
+      return std::__copy_move_backward<_IsMove,
+           __memcpyable<_BI2, _BI1>::__value,
+           _Category>::__copy_move_b(__first,
+         __last,
+         __result);
+    }
+
+  template<bool _IsMove, typename _BI1, typename _BI2>
+   
+    inline _BI2
+    __copy_move_backward_a1(_BI1 __first, _BI1 __last, _BI2 __result)
+    { return std::__copy_move_backward_a2<_IsMove>(__first, __last, __result); }
+
+  template<bool _IsMove,
+    typename _Tp, typename _Ref, typename _Ptr, typename _OI>
+    _OI
+    __copy_move_backward_a1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+       std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+       _OI);
+
+  template<bool _IsMove,
+    typename _ITp, typename _IRef, typename _IPtr, typename _OTp>
+    std::_Deque_iterator<_OTp, _OTp&, _OTp*>
+    __copy_move_backward_a1(
+   std::_Deque_iterator<_ITp, _IRef, _IPtr>,
+   std::_Deque_iterator<_ITp, _IRef, _IPtr>,
+   std::_Deque_iterator<_OTp, _OTp&, _OTp*>);
+
+  template<bool _IsMove, typename _II, typename _Tp>
+    typename __gnu_cxx::__enable_if<
+      __is_random_access_iter<_II>::__value,
+      std::_Deque_iterator<_Tp, _Tp&, _Tp*> >::__type
+    __copy_move_backward_a1(_II, _II,
+       std::_Deque_iterator<_Tp, _Tp&, _Tp*>);
+
+  template<bool _IsMove, typename _II, typename _OI>
+   
+    inline _OI
+    __copy_move_backward_a(_II __first, _II __last, _OI __result)
+    {
+      return std::__niter_wrap(__result,
+  std::__copy_move_backward_a1<_IsMove>
+    (std::__niter_base(__first), std::__niter_base(__last),
+     std::__niter_base(__result)));
+    }
+
+  template<bool _IsMove,
+    typename _Ite, typename _Seq, typename _Cat, typename _OI>
+    _OI
+    __copy_move_backward_a(
+  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+  _OI);
+
+  template<bool _IsMove,
+    typename _II, typename _Ite, typename _Seq, typename _Cat>
+    __gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
+    __copy_move_backward_a(_II, _II,
+  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&);
+
+  template<bool _IsMove,
+    typename _IIte, typename _ISeq, typename _ICat,
+    typename _OIte, typename _OSeq, typename _OCat>
+    ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>
+    __copy_move_backward_a(
+  const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
+  const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
+  const ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>&);
+# 854 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _BI1, typename _BI2>
+   
+    inline _BI2
+    copy_backward(_BI1 __first, _BI1 __last, _BI2 __result)
+    {
+
+     
+     
+     
+
+      ;
+
+      return std::__copy_move_backward_a<__is_move_iterator<_BI1>::__value>
+      (std::__miter_base(__first), std::__miter_base(__last), __result);
+    }
+# 889 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _BI1, typename _BI2>
+   
+    inline _BI2
+    move_backward(_BI1 __first, _BI1 __last, _BI2 __result)
+    {
+
+     
+     
+     
+
+      ;
+
+      return std::__copy_move_backward_a<true>(std::__miter_base(__first),
+            std::__miter_base(__last),
+            __result);
+    }
+
+
+
+
+
+
+  template<typename _ForwardIterator, typename _Tp>
+   
+    inline typename
+    __gnu_cxx::__enable_if<!__is_scalar<_Tp>::__value, void>::__type
+    __fill_a1(_ForwardIterator __first, _ForwardIterator __last,
+       const _Tp& __value)
+    {
+      for (; __first != __last; ++__first)
+ *__first = __value;
+    }
+
+  template<typename _ForwardIterator, typename _Tp>
+   
+    inline typename
+    __gnu_cxx::__enable_if<__is_scalar<_Tp>::__value, void>::__type
+    __fill_a1(_ForwardIterator __first, _ForwardIterator __last,
+       const _Tp& __value)
+    {
+      const _Tp __tmp = __value;
+      for (; __first != __last; ++__first)
+ *__first = __tmp;
+    }
+
+
+  template<typename _Tp>
+   
+    inline typename
+    __gnu_cxx::__enable_if<__is_byte<_Tp>::__value, void>::__type
+    __fill_a1(_Tp* __first, _Tp* __last, const _Tp& __c)
+    {
+      const _Tp __tmp = __c;
+# 950 "/usr/include/c++/13/bits/stl_algobase.h" 3
+      if (const size_t __len = __last - __first)
+ __builtin_memset(__first, static_cast<unsigned char>(__tmp), __len);
+    }
+
+  template<typename _Ite, typename _Cont, typename _Tp>
+   
+    inline void
+    __fill_a1(::__gnu_cxx::__normal_iterator<_Ite, _Cont> __first,
+       ::__gnu_cxx::__normal_iterator<_Ite, _Cont> __last,
+       const _Tp& __value)
+    { std::__fill_a1(__first.base(), __last.base(), __value); }
+
+  template<typename _Tp, typename _VTp>
+    void
+    __fill_a1(const std::_Deque_iterator<_Tp, _Tp&, _Tp*>&,
+       const std::_Deque_iterator<_Tp, _Tp&, _Tp*>&,
+       const _VTp&);
+
+ 
+  void
+  __fill_a1(std::_Bit_iterator, std::_Bit_iterator,
+     const bool&);
+
+  template<typename _FIte, typename _Tp>
+   
+    inline void
+    __fill_a(_FIte __first, _FIte __last, const _Tp& __value)
+    { std::__fill_a1(__first, __last, __value); }
+
+  template<typename _Ite, typename _Seq, typename _Cat, typename _Tp>
+    void
+    __fill_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+      const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
+      const _Tp&);
+# 997 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _ForwardIterator, typename _Tp>
+   
+    inline void
+    fill(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value)
+    {
+
+     
+
+      ;
+
+      std::__fill_a(__first, __last, __value);
+    }
+
+
+  inline constexpr int
+  __size_to_integer(int __n) { return __n; }
+  inline constexpr unsigned
+  __size_to_integer(unsigned __n) { return __n; }
+  inline constexpr long
+  __size_to_integer(long __n) { return __n; }
+  inline constexpr unsigned long
+  __size_to_integer(unsigned long __n) { return __n; }
+  inline constexpr long long
+  __size_to_integer(long long __n) { return __n; }
+  inline constexpr unsigned long long
+  __size_to_integer(unsigned long long __n) { return __n; }
+
+
+  __extension__ inline constexpr __int128
+  __size_to_integer(__int128 __n) { return __n; }
+  __extension__ inline constexpr unsigned __int128
+  __size_to_integer(unsigned __int128 __n) { return __n; }
+# 1049 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  inline constexpr long long
+  __size_to_integer(float __n) { return (long long)__n; }
+  inline constexpr long long
+  __size_to_integer(double __n) { return (long long)__n; }
+  inline constexpr long long
+  __size_to_integer(long double __n) { return (long long)__n; }
+
+
+
+
+
+  template<typename _OutputIterator, typename _Size, typename _Tp>
+   
+    inline typename
+    __gnu_cxx::__enable_if<!__is_scalar<_Tp>::__value, _OutputIterator>::__type
+    __fill_n_a1(_OutputIterator __first, _Size __n, const _Tp& __value)
+    {
+      for (; __n > 0; --__n, (void) ++__first)
+ *__first = __value;
+      return __first;
+    }
+
+  template<typename _OutputIterator, typename _Size, typename _Tp>
+   
+    inline typename
+    __gnu_cxx::__enable_if<__is_scalar<_Tp>::__value, _OutputIterator>::__type
+    __fill_n_a1(_OutputIterator __first, _Size __n, const _Tp& __value)
+    {
+      const _Tp __tmp = __value;
+      for (; __n > 0; --__n, (void) ++__first)
+ *__first = __tmp;
+      return __first;
+    }
+
+  template<typename _Ite, typename _Seq, typename _Cat, typename _Size,
+    typename _Tp>
+    ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
+    __fill_n_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>& __first,
+        _Size __n, const _Tp& __value,
+        std::input_iterator_tag);
+
+  template<typename _OutputIterator, typename _Size, typename _Tp>
+   
+    inline _OutputIterator
+    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
+        std::output_iterator_tag)
+    {
+
+      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");
+
+      return __fill_n_a1(__first, __n, __value);
+    }
+
+  template<typename _OutputIterator, typename _Size, typename _Tp>
+   
+    inline _OutputIterator
+    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
+        std::input_iterator_tag)
+    {
+
+      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");
+
+      return __fill_n_a1(__first, __n, __value);
+    }
+
+  template<typename _OutputIterator, typename _Size, typename _Tp>
+   
+    inline _OutputIterator
+    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
+        std::random_access_iterator_tag)
+    {
+
+      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");
+
+      if (__n <= 0)
+ return __first;
+
+      ;
+
+      std::__fill_a(__first, __first + __n, __value);
+      return __first + __n;
+    }
+# 1149 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _OI, typename _Size, typename _Tp>
+   
+    inline _OI
+    fill_n(_OI __first, _Size __n, const _Tp& __value)
+    {
+
+     
+
+      return std::__fill_n_a(__first, std::__size_to_integer(__n), __value,
+          std::__iterator_category(__first));
+    }
+
+  template<bool _BoolType>
+    struct __equal
+    {
+      template<typename _II1, typename _II2>
+
+ static bool
+ equal(_II1 __first1, _II1 __last1, _II2 __first2)
+ {
+   for (; __first1 != __last1; ++__first1, (void) ++__first2)
+     if (!(*__first1 == *__first2))
+       return false;
+   return true;
+ }
+    };
+
+  template<>
+    struct __equal<true>
+    {
+      template<typename _Tp>
+
+ static bool
+ equal(const _Tp* __first1, const _Tp* __last1, const _Tp* __first2)
+ {
+   if (const size_t __len = (__last1 - __first1))
+     return !std::__memcmp(__first1, __first2, __len);
+   return true;
+ }
+    };
+
+  template<typename _Tp, typename _Ref, typename _Ptr, typename _II>
+    typename __gnu_cxx::__enable_if<
+      __is_random_access_iter<_II>::__value, bool>::__type
+    __equal_aux1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+   std::_Deque_iterator<_Tp, _Ref, _Ptr>,
+   _II);
+
+  template<typename _Tp1, typename _Ref1, typename _Ptr1,
+    typename _Tp2, typename _Ref2, typename _Ptr2>
+    bool
+    __equal_aux1(std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+   std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+   std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);
+
+  template<typename _II, typename _Tp, typename _Ref, typename _Ptr>
+    typename __gnu_cxx::__enable_if<
+      __is_random_access_iter<_II>::__value, bool>::__type
+    __equal_aux1(_II, _II,
+  std::_Deque_iterator<_Tp, _Ref, _Ptr>);
+
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    __equal_aux1(_II1 __first1, _II1 __last1, _II2 __first2)
+    {
+      typedef typename iterator_traits<_II1>::value_type _ValueType1;
+      const bool __simple = ((__is_integer<_ValueType1>::__value
+         || __is_pointer<_ValueType1>::__value)
+        && __memcmpable<_II1, _II2>::__value);
+      return std::__equal<__simple>::equal(__first1, __last1, __first2);
+    }
+
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    __equal_aux(_II1 __first1, _II1 __last1, _II2 __first2)
+    {
+      return std::__equal_aux1(std::__niter_base(__first1),
+          std::__niter_base(__last1),
+          std::__niter_base(__first2));
+    }
+
+  template<typename _II1, typename _Seq1, typename _Cat1, typename _II2>
+    bool
+    __equal_aux(const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
+  _II2);
+
+  template<typename _II1, typename _II2, typename _Seq2, typename _Cat2>
+    bool
+    __equal_aux(_II1, _II1,
+  const ::__gnu_debug::_Safe_iterator<_II2, _Seq2, _Cat2>&);
+
+  template<typename _II1, typename _Seq1, typename _Cat1,
+    typename _II2, typename _Seq2, typename _Cat2>
+    bool
+    __equal_aux(const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_II2, _Seq2, _Cat2>&);
+
+  template<typename, typename>
+    struct __lc_rai
+    {
+      template<typename _II1, typename _II2>
+
+ static _II1
+ __newlast1(_II1, _II1 __last1, _II2, _II2)
+ { return __last1; }
+
+      template<typename _II>
+
+ static bool
+ __cnd2(_II __first, _II __last)
+ { return __first != __last; }
+    };
+
+  template<>
+    struct __lc_rai<random_access_iterator_tag, random_access_iterator_tag>
+    {
+      template<typename _RAI1, typename _RAI2>
+
+ static _RAI1
+ __newlast1(_RAI1 __first1, _RAI1 __last1,
+     _RAI2 __first2, _RAI2 __last2)
+ {
+   const typename iterator_traits<_RAI1>::difference_type
+     __diff1 = __last1 - __first1;
+   const typename iterator_traits<_RAI2>::difference_type
+     __diff2 = __last2 - __first2;
+   return __diff2 < __diff1 ? __first1 + __diff2 : __last1;
+ }
+
+      template<typename _RAI>
+ static bool
+ __cnd2(_RAI, _RAI)
+ { return true; }
+    };
+
+  template<typename _II1, typename _II2, typename _Compare>
+   
+    bool
+    __lexicographical_compare_impl(_II1 __first1, _II1 __last1,
+       _II2 __first2, _II2 __last2,
+       _Compare __comp)
+    {
+      typedef typename iterator_traits<_II1>::iterator_category _Category1;
+      typedef typename iterator_traits<_II2>::iterator_category _Category2;
+      typedef std::__lc_rai<_Category1, _Category2> __rai_type;
+
+      __last1 = __rai_type::__newlast1(__first1, __last1, __first2, __last2);
+      for (; __first1 != __last1 && __rai_type::__cnd2(__first2, __last2);
+    ++__first1, (void)++__first2)
+ {
+   if (__comp(__first1, __first2))
+     return true;
+   if (__comp(__first2, __first1))
+     return false;
+ }
+      return __first1 == __last1 && __first2 != __last2;
+    }
+
+  template<bool _BoolType>
+    struct __lexicographical_compare
+    {
+      template<typename _II1, typename _II2>
+
+ static bool
+ __lc(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
+ {
+   using __gnu_cxx::__ops::__iter_less_iter;
+   return std::__lexicographical_compare_impl(__first1, __last1,
+           __first2, __last2,
+           __iter_less_iter());
+ }
+
+      template<typename _II1, typename _II2>
+
+ static int
+ __3way(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
+ {
+   while (__first1 != __last1)
+     {
+       if (__first2 == __last2)
+  return +1;
+       if (*__first1 < *__first2)
+  return -1;
+       if (*__first2 < *__first1)
+  return +1;
+       ++__first1;
+       ++__first2;
+     }
+   return int(__first2 == __last2) - 1;
+ }
+    };
+
+  template<>
+    struct __lexicographical_compare<true>
+    {
+      template<typename _Tp, typename _Up>
+
+ static bool
+ __lc(const _Tp* __first1, const _Tp* __last1,
+      const _Up* __first2, const _Up* __last2)
+ { return __3way(__first1, __last1, __first2, __last2) < 0; }
+
+      template<typename _Tp, typename _Up>
+
+ static ptrdiff_t
+ __3way(const _Tp* __first1, const _Tp* __last1,
+        const _Up* __first2, const _Up* __last2)
+ {
+   const size_t __len1 = __last1 - __first1;
+   const size_t __len2 = __last2 - __first2;
+   if (const size_t __len = std::min(__len1, __len2))
+     if (int __result = std::__memcmp(__first1, __first2, __len))
+       return __result;
+   return ptrdiff_t(__len1 - __len2);
+ }
+    };
+
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    __lexicographical_compare_aux1(_II1 __first1, _II1 __last1,
+       _II2 __first2, _II2 __last2)
+    {
+      typedef typename iterator_traits<_II1>::value_type _ValueType1;
+      typedef typename iterator_traits<_II2>::value_type _ValueType2;
+      const bool __simple =
+ (__is_memcmp_ordered_with<_ValueType1, _ValueType2>::__value
+  && __is_pointer<_II1>::__value
+  && __is_pointer<_II2>::__value
+
+
+
+
+
+
+
+  );
+
+      return std::__lexicographical_compare<__simple>::__lc(__first1, __last1,
+           __first2, __last2);
+    }
+
+  template<typename _Tp1, typename _Ref1, typename _Ptr1,
+    typename _Tp2>
+    bool
+    __lexicographical_compare_aux1(
+ std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+ std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+ _Tp2*, _Tp2*);
+
+  template<typename _Tp1,
+    typename _Tp2, typename _Ref2, typename _Ptr2>
+    bool
+    __lexicographical_compare_aux1(_Tp1*, _Tp1*,
+ std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>,
+ std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);
+
+  template<typename _Tp1, typename _Ref1, typename _Ptr1,
+    typename _Tp2, typename _Ref2, typename _Ptr2>
+    bool
+    __lexicographical_compare_aux1(
+ std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+ std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
+ std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>,
+ std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);
+
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    __lexicographical_compare_aux(_II1 __first1, _II1 __last1,
+      _II2 __first2, _II2 __last2)
+    {
+      return std::__lexicographical_compare_aux1(std::__niter_base(__first1),
+       std::__niter_base(__last1),
+       std::__niter_base(__first2),
+       std::__niter_base(__last2));
+    }
+
+  template<typename _Iter1, typename _Seq1, typename _Cat1,
+    typename _II2>
+    bool
+    __lexicographical_compare_aux(
+  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
+  _II2, _II2);
+
+  template<typename _II1,
+    typename _Iter2, typename _Seq2, typename _Cat2>
+    bool
+    __lexicographical_compare_aux(
+  _II1, _II1,
+  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&,
+  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&);
+
+  template<typename _Iter1, typename _Seq1, typename _Cat1,
+    typename _Iter2, typename _Seq2, typename _Cat2>
+    bool
+    __lexicographical_compare_aux(
+  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
+  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&,
+  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&);
+
+  template<typename _ForwardIterator, typename _Tp, typename _Compare>
+   
+    _ForwardIterator
+    __lower_bound(_ForwardIterator __first, _ForwardIterator __last,
+    const _Tp& __val, _Compare __comp)
+    {
+      typedef typename iterator_traits<_ForwardIterator>::difference_type
+ _DistanceType;
+
+      _DistanceType __len = std::distance(__first, __last);
+
+      while (__len > 0)
+ {
+   _DistanceType __half = __len >> 1;
+   _ForwardIterator __middle = __first;
+   std::advance(__middle, __half);
+   if (__comp(__middle, __val))
+     {
+       __first = __middle;
+       ++__first;
+       __len = __len - __half - 1;
+     }
+   else
+     __len = __half;
+ }
+      return __first;
+    }
+# 1495 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _ForwardIterator, typename _Tp>
+   
+    inline _ForwardIterator
+    lower_bound(_ForwardIterator __first, _ForwardIterator __last,
+  const _Tp& __val)
+    {
+
+     
+     
+
+      ;
+
+      return std::__lower_bound(__first, __last, __val,
+    __gnu_cxx::__ops::__iter_less_val());
+    }
+
+
+
+  template<typename _Tp>
+    inline constexpr _Tp
+    __lg(_Tp __n)
+    {
+
+      return std::__bit_width(make_unsigned_t<_Tp>(__n)) - 1;
+# 1528 "/usr/include/c++/13/bits/stl_algobase.h" 3
+    }
+
+
+# 1544 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    equal(_II1 __first1, _II1 __last1, _II2 __first2)
+    {
+
+     
+     
+     
+
+
+      ;
+
+      return std::__equal_aux(__first1, __last1, __first2);
+    }
+# 1575 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _IIter1, typename _IIter2, typename _BinaryPredicate>
+   
+    inline bool
+    equal(_IIter1 __first1, _IIter1 __last1,
+   _IIter2 __first2, _BinaryPredicate __binary_pred)
+    {
+
+     
+     
+      ;
+
+      for (; __first1 != __last1; ++__first1, (void)++__first2)
+ if (!bool(__binary_pred(*__first1, *__first2)))
+   return false;
+      return true;
+    }
+
+
+
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    __equal4(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
+    {
+      using _RATag = random_access_iterator_tag;
+      using _Cat1 = typename iterator_traits<_II1>::iterator_category;
+      using _Cat2 = typename iterator_traits<_II2>::iterator_category;
+      using _RAIters = __and_<is_same<_Cat1, _RATag>, is_same<_Cat2, _RATag>>;
+      if (_RAIters())
+ {
+   auto __d1 = std::distance(__first1, __last1);
+   auto __d2 = std::distance(__first2, __last2);
+   if (__d1 != __d2)
+     return false;
+   return std::equal(__first1, __last1, __first2);
+ }
+
+      for (; __first1 != __last1 && __first2 != __last2;
+   ++__first1, (void)++__first2)
+ if (!(*__first1 == *__first2))
+   return false;
+      return __first1 == __last1 && __first2 == __last2;
+    }
+
+
+  template<typename _II1, typename _II2, typename _BinaryPredicate>
+   
+    inline bool
+    __equal4(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2,
+      _BinaryPredicate __binary_pred)
+    {
+      using _RATag = random_access_iterator_tag;
+      using _Cat1 = typename iterator_traits<_II1>::iterator_category;
+      using _Cat2 = typename iterator_traits<_II2>::iterator_category;
+      using _RAIters = __and_<is_same<_Cat1, _RATag>, is_same<_Cat2, _RATag>>;
+      if (_RAIters())
+ {
+   auto __d1 = std::distance(__first1, __last1);
+   auto __d2 = std::distance(__first2, __last2);
+   if (__d1 != __d2)
+     return false;
+   return std::equal(__first1, __last1, __first2,
+           __binary_pred);
+ }
+
+      for (; __first1 != __last1 && __first2 != __last2;
+   ++__first1, (void)++__first2)
+ if (!bool(__binary_pred(*__first1, *__first2)))
+   return false;
+      return __first1 == __last1 && __first2 == __last2;
+    }
+# 1665 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    equal(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
+    {
+
+     
+     
+     
+
+
+      ;
+      ;
+
+      return std::__equal4(__first1, __last1, __first2, __last2);
+    }
+# 1698 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _IIter1, typename _IIter2, typename _BinaryPredicate>
+   
+    inline bool
+    equal(_IIter1 __first1, _IIter1 __last1,
+   _IIter2 __first2, _IIter2 __last2, _BinaryPredicate __binary_pred)
+    {
+
+     
+     
+      ;
+      ;
+
+      return std::__equal4(__first1, __last1, __first2, __last2,
+          __binary_pred);
+    }
+# 1730 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II1, typename _II2>
+   
+    inline bool
+    lexicographical_compare(_II1 __first1, _II1 __last1,
+       _II2 __first2, _II2 __last2)
+    {
+
+
+
+
+
+     
+     
+     
+     
+      ;
+      ;
+
+      return std::__lexicographical_compare_aux(__first1, __last1,
+      __first2, __last2);
+    }
+# 1765 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _II1, typename _II2, typename _Compare>
+   
+    inline bool
+    lexicographical_compare(_II1 __first1, _II1 __last1,
+       _II2 __first2, _II2 __last2, _Compare __comp)
+    {
+
+     
+     
+      ;
+      ;
+
+      return std::__lexicographical_compare_impl
+ (__first1, __last1, __first2, __last2,
+  __gnu_cxx::__ops::__iter_comp_iter(__comp));
+    }
+# 1880 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _InputIterator1, typename _InputIterator2,
+    typename _BinaryPredicate>
+   
+    pair<_InputIterator1, _InputIterator2>
+    __mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+        _InputIterator2 __first2, _BinaryPredicate __binary_pred)
+    {
+      while (__first1 != __last1 && __binary_pred(__first1, __first2))
+ {
+   ++__first1;
+   ++__first2;
+ }
+      return pair<_InputIterator1, _InputIterator2>(__first1, __first2);
+    }
+# 1908 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _InputIterator1, typename _InputIterator2>
+   
+    inline pair<_InputIterator1, _InputIterator2>
+    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+      _InputIterator2 __first2)
+    {
+
+     
+     
+     
+
+
+      ;
+
+      return std::__mismatch(__first1, __last1, __first2,
+        __gnu_cxx::__ops::__iter_equal_to_iter());
+    }
+# 1942 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _InputIterator1, typename _InputIterator2,
+    typename _BinaryPredicate>
+   
+    inline pair<_InputIterator1, _InputIterator2>
+    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+      _InputIterator2 __first2, _BinaryPredicate __binary_pred)
+    {
+
+     
+     
+      ;
+
+      return std::__mismatch(__first1, __last1, __first2,
+ __gnu_cxx::__ops::__iter_comp_iter(__binary_pred));
+    }
+
+
+
+  template<typename _InputIterator1, typename _InputIterator2,
+    typename _BinaryPredicate>
+   
+    pair<_InputIterator1, _InputIterator2>
+    __mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+        _InputIterator2 __first2, _InputIterator2 __last2,
+        _BinaryPredicate __binary_pred)
+    {
+      while (__first1 != __last1 && __first2 != __last2
+      && __binary_pred(__first1, __first2))
+ {
+   ++__first1;
+   ++__first2;
+ }
+      return pair<_InputIterator1, _InputIterator2>(__first1, __first2);
+    }
+# 1991 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _InputIterator1, typename _InputIterator2>
+   
+    inline pair<_InputIterator1, _InputIterator2>
+    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+      _InputIterator2 __first2, _InputIterator2 __last2)
+    {
+
+     
+     
+     
+
+
+      ;
+      ;
+
+      return std::__mismatch(__first1, __last1, __first2, __last2,
+        __gnu_cxx::__ops::__iter_equal_to_iter());
+    }
+# 2027 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _InputIterator1, typename _InputIterator2,
+    typename _BinaryPredicate>
+   
+    inline pair<_InputIterator1, _InputIterator2>
+    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
+      _InputIterator2 __first2, _InputIterator2 __last2,
+      _BinaryPredicate __binary_pred)
+    {
+
+     
+     
+      ;
+      ;
+
+      return std::__mismatch(__first1, __last1, __first2, __last2,
+        __gnu_cxx::__ops::__iter_comp_iter(__binary_pred));
+    }
+
+
+
+
+
+  template<typename _InputIterator, typename _Predicate>
+   
+    inline _InputIterator
+    __find_if(_InputIterator __first, _InputIterator __last,
+       _Predicate __pred, input_iterator_tag)
+    {
+      while (__first != __last && !__pred(__first))
+ ++__first;
+      return __first;
+    }
+
+
+  template<typename _RandomAccessIterator, typename _Predicate>
+   
+    _RandomAccessIterator
+    __find_if(_RandomAccessIterator __first, _RandomAccessIterator __last,
+       _Predicate __pred, random_access_iterator_tag)
+    {
+      typename iterator_traits<_RandomAccessIterator>::difference_type
+ __trip_count = (__last - __first) >> 2;
+
+      for (; __trip_count > 0; --__trip_count)
+ {
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+   if (__pred(__first))
+     return __first;
+   ++__first;
+ }
+
+      switch (__last - __first)
+ {
+ case 3:
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+ case 2:
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+ case 1:
+   if (__pred(__first))
+     return __first;
+   ++__first;
+
+ case 0:
+ default:
+   return __last;
+ }
+    }
+
+  template<typename _Iterator, typename _Predicate>
+   
+    inline _Iterator
+    __find_if(_Iterator __first, _Iterator __last, _Predicate __pred)
+    {
+      return __find_if(__first, __last, __pred,
+         std::__iterator_category(__first));
+    }
+
+  template<typename _InputIterator, typename _Predicate>
+   
+    typename iterator_traits<_InputIterator>::difference_type
+    __count_if(_InputIterator __first, _InputIterator __last, _Predicate __pred)
+    {
+      typename iterator_traits<_InputIterator>::difference_type __n = 0;
+      for (; __first != __last; ++__first)
+ if (__pred(__first))
+   ++__n;
+      return __n;
+    }
+
+  template<typename _ForwardIterator, typename _Predicate>
+   
+    _ForwardIterator
+    __remove_if(_ForwardIterator __first, _ForwardIterator __last,
+  _Predicate __pred)
+    {
+      __first = std::__find_if(__first, __last, __pred);
+      if (__first == __last)
+ return __first;
+      _ForwardIterator __result = __first;
+      ++__first;
+      for (; __first != __last; ++__first)
+ if (!__pred(__first))
+   {
+     *__result = std::move(*__first);
+     ++__result;
+   }
+      return __result;
+    }
+
+
+  template<typename _ForwardIterator1, typename _ForwardIterator2,
+    typename _BinaryPredicate>
+   
+    bool
+    __is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
+       _ForwardIterator2 __first2, _BinaryPredicate __pred)
+    {
+
+
+      for (; __first1 != __last1; ++__first1, (void)++__first2)
+ if (!__pred(__first1, __first2))
+   break;
+
+      if (__first1 == __last1)
+ return true;
+
+
+
+      _ForwardIterator2 __last2 = __first2;
+      std::advance(__last2, std::distance(__first1, __last1));
+      for (_ForwardIterator1 __scan = __first1; __scan != __last1; ++__scan)
+ {
+   if (__scan != std::__find_if(__first1, __scan,
+     __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan)))
+     continue;
+
+   auto __matches
+     = std::__count_if(__first2, __last2,
+   __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan));
+   if (0 == __matches ||
+       std::__count_if(__scan, __last1,
+   __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan))
+       != __matches)
+     return false;
+ }
+      return true;
+    }
+# 2204 "/usr/include/c++/13/bits/stl_algobase.h" 3
+  template<typename _ForwardIterator1, typename _ForwardIterator2>
+   
+    inline bool
+    is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
+     _ForwardIterator2 __first2)
+    {
+
+     
+     
+     
+
+
+      ;
+
+      return std::__is_permutation(__first1, __last1, __first2,
+       __gnu_cxx::__ops::__iter_equal_to_iter());
+    }
+
+
+
+}
+# 44 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/limits" 1 3
+# 40 "/usr/include/c++/13/limits" 3
+       
+# 41 "/usr/include/c++/13/limits" 3
+# 158 "/usr/include/c++/13/limits" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+
+
+
+
+  enum float_round_style
+  {
+    round_indeterminate = -1,
+    round_toward_zero = 0,
+    round_to_nearest = 1,
+    round_toward_infinity = 2,
+    round_toward_neg_infinity = 3
+  };
+
+
+
+
+
+
+
+  enum float_denorm_style
+  {
+
+    denorm_indeterminate = -1,
+
+    denorm_absent = 0,
+
+    denorm_present = 1
+  };
+# 202 "/usr/include/c++/13/limits" 3
+  struct __numeric_limits_base
+  {
+
+
+    static constexpr bool is_specialized = false;
+
+
+
+
+    static constexpr int digits = 0;
+
+
+    static constexpr int digits10 = 0;
+
+
+
+
+    static constexpr int max_digits10 = 0;
+
+
+
+    static constexpr bool is_signed = false;
+
+
+    static constexpr bool is_integer = false;
+
+
+
+
+    static constexpr bool is_exact = false;
+
+
+
+    static constexpr int radix = 0;
+
+
+
+    static constexpr int min_exponent = 0;
+
+
+
+    static constexpr int min_exponent10 = 0;
+
+
+
+
+    static constexpr int max_exponent = 0;
+
+
+
+    static constexpr int max_exponent10 = 0;
+
+
+    static constexpr bool has_infinity = false;
+
+
+
+    static constexpr bool has_quiet_NaN = false;
+
+
+
+    static constexpr bool has_signaling_NaN = false;
+
+
+    static constexpr float_denorm_style has_denorm = denorm_absent;
+
+
+
+    static constexpr bool has_denorm_loss = false;
+
+
+
+    static constexpr bool is_iec559 = false;
+
+
+
+
+    static constexpr bool is_bounded = false;
+# 288 "/usr/include/c++/13/limits" 3
+    static constexpr bool is_modulo = false;
+
+
+    static constexpr bool traps = false;
+
+
+    static constexpr bool tinyness_before = false;
+
+
+
+
+    static constexpr float_round_style round_style =
+          round_toward_zero;
+  };
+# 311 "/usr/include/c++/13/limits" 3
+  template<typename _Tp>
+    struct numeric_limits : public __numeric_limits_base
+    {
+
+
+      static constexpr _Tp
+      min() noexcept { return _Tp(); }
+
+
+      static constexpr _Tp
+      max() noexcept { return _Tp(); }
+
+
+
+
+      static constexpr _Tp
+      lowest() noexcept { return _Tp(); }
+
+
+
+
+      static constexpr _Tp
+      epsilon() noexcept { return _Tp(); }
+
+
+      static constexpr _Tp
+      round_error() noexcept { return _Tp(); }
+
+
+      static constexpr _Tp
+      infinity() noexcept { return _Tp(); }
+
+
+
+      static constexpr _Tp
+      quiet_NaN() noexcept { return _Tp(); }
+
+
+
+      static constexpr _Tp
+      signaling_NaN() noexcept { return _Tp(); }
+
+
+
+
+      static constexpr _Tp
+      denorm_min() noexcept { return _Tp(); }
+    };
+
+
+
+
+  template<typename _Tp>
+    struct numeric_limits<const _Tp>
+    : public numeric_limits<_Tp> { };
+
+  template<typename _Tp>
+    struct numeric_limits<volatile _Tp>
+    : public numeric_limits<_Tp> { };
+
+  template<typename _Tp>
+    struct numeric_limits<const volatile _Tp>
+    : public numeric_limits<_Tp> { };
+# 383 "/usr/include/c++/13/limits" 3
+  template<>
+    struct numeric_limits<bool>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr bool
+      min() noexcept { return false; }
+
+      static constexpr bool
+      max() noexcept { return true; }
+
+
+      static constexpr bool
+      lowest() noexcept { return min(); }
+
+      static constexpr int digits = 1;
+      static constexpr int digits10 = 0;
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr bool
+      epsilon() noexcept { return false; }
+
+      static constexpr bool
+      round_error() noexcept { return false; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr bool
+      infinity() noexcept { return false; }
+
+      static constexpr bool
+      quiet_NaN() noexcept { return false; }
+
+      static constexpr bool
+      signaling_NaN() noexcept { return false; }
+
+      static constexpr bool
+      denorm_min() noexcept { return false; }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+
+
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<char>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr char
+      min() noexcept { return (((char)(-1) < 0) ? -(((char)(-1) < 0) ? (((((char)1 << ((sizeof(char) * 8 - ((char)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char)0) - 1 : (char)0); }
+
+      static constexpr char
+      max() noexcept { return (((char)(-1) < 0) ? (((((char)1 << ((sizeof(char) * 8 - ((char)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char)0); }
+
+
+      static constexpr char
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(char) * 8 - ((char)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(char) * 8 - ((char)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = ((char)(-1) < 0);
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr char
+      epsilon() noexcept { return 0; }
+
+      static constexpr char
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr
+      char infinity() noexcept { return char(); }
+
+      static constexpr char
+      quiet_NaN() noexcept { return char(); }
+
+      static constexpr char
+      signaling_NaN() noexcept { return char(); }
+
+      static constexpr char
+      denorm_min() noexcept { return static_cast<char>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = !is_signed;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<signed char>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr signed char
+      min() noexcept { return -0x7f - 1; }
+
+      static constexpr signed char
+      max() noexcept { return 0x7f; }
+
+
+      static constexpr signed char
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(signed char) * 8 - ((signed char)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(signed char) * 8 - ((signed char)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr signed char
+      epsilon() noexcept { return 0; }
+
+      static constexpr signed char
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr signed char
+      infinity() noexcept { return static_cast<signed char>(0); }
+
+      static constexpr signed char
+      quiet_NaN() noexcept { return static_cast<signed char>(0); }
+
+      static constexpr signed char
+      signaling_NaN() noexcept
+      { return static_cast<signed char>(0); }
+
+      static constexpr signed char
+      denorm_min() noexcept
+      { return static_cast<signed char>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<unsigned char>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr unsigned char
+      min() noexcept { return 0; }
+
+      static constexpr unsigned char
+      max() noexcept { return 0x7f * 2U + 1; }
+
+
+      static constexpr unsigned char
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(unsigned char) * 8 - ((unsigned char)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(unsigned char) * 8 - ((unsigned char)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr unsigned char
+      epsilon() noexcept { return 0; }
+
+      static constexpr unsigned char
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr unsigned char
+      infinity() noexcept
+      { return static_cast<unsigned char>(0); }
+
+      static constexpr unsigned char
+      quiet_NaN() noexcept
+      { return static_cast<unsigned char>(0); }
+
+      static constexpr unsigned char
+      signaling_NaN() noexcept
+      { return static_cast<unsigned char>(0); }
+
+      static constexpr unsigned char
+      denorm_min() noexcept
+      { return static_cast<unsigned char>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = true;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<wchar_t>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr wchar_t
+      min() noexcept { return (((wchar_t)(-1) < 0) ? -(((wchar_t)(-1) < 0) ? (((((wchar_t)1 << ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(wchar_t)0) - 1 : (wchar_t)0); }
+
+      static constexpr wchar_t
+      max() noexcept { return (((wchar_t)(-1) < 0) ? (((((wchar_t)1 << ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(wchar_t)0); }
+
+
+      static constexpr wchar_t
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = ((wchar_t)(-1) < 0);
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr wchar_t
+      epsilon() noexcept { return 0; }
+
+      static constexpr wchar_t
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr wchar_t
+      infinity() noexcept { return wchar_t(); }
+
+      static constexpr wchar_t
+      quiet_NaN() noexcept { return wchar_t(); }
+
+      static constexpr wchar_t
+      signaling_NaN() noexcept { return wchar_t(); }
+
+      static constexpr wchar_t
+      denorm_min() noexcept { return wchar_t(); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = !is_signed;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+# 796 "/usr/include/c++/13/limits" 3
+  template<>
+    struct numeric_limits<char16_t>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr char16_t
+      min() noexcept { return (((char16_t)(-1) < 0) ? -(((char16_t)(-1) < 0) ? (((((char16_t)1 << ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char16_t)0) - 1 : (char16_t)0); }
+
+      static constexpr char16_t
+      max() noexcept { return (((char16_t)(-1) < 0) ? (((((char16_t)1 << ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char16_t)0); }
+
+      static constexpr char16_t
+      lowest() noexcept { return min(); }
+
+      static constexpr int digits = (sizeof(char16_t) * 8 - ((char16_t)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) * 643L / 2136);
+      static constexpr int max_digits10 = 0;
+      static constexpr bool is_signed = ((char16_t)(-1) < 0);
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr char16_t
+      epsilon() noexcept { return 0; }
+
+      static constexpr char16_t
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr char16_t
+      infinity() noexcept { return char16_t(); }
+
+      static constexpr char16_t
+      quiet_NaN() noexcept { return char16_t(); }
+
+      static constexpr char16_t
+      signaling_NaN() noexcept { return char16_t(); }
+
+      static constexpr char16_t
+      denorm_min() noexcept { return char16_t(); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = !is_signed;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<char32_t>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr char32_t
+      min() noexcept { return (((char32_t)(-1) < 0) ? -(((char32_t)(-1) < 0) ? (((((char32_t)1 << ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char32_t)0) - 1 : (char32_t)0); }
+
+      static constexpr char32_t
+      max() noexcept { return (((char32_t)(-1) < 0) ? (((((char32_t)1 << ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char32_t)0); }
+
+      static constexpr char32_t
+      lowest() noexcept { return min(); }
+
+      static constexpr int digits = (sizeof(char32_t) * 8 - ((char32_t)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) * 643L / 2136);
+      static constexpr int max_digits10 = 0;
+      static constexpr bool is_signed = ((char32_t)(-1) < 0);
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr char32_t
+      epsilon() noexcept { return 0; }
+
+      static constexpr char32_t
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr char32_t
+      infinity() noexcept { return char32_t(); }
+
+      static constexpr char32_t
+      quiet_NaN() noexcept { return char32_t(); }
+
+      static constexpr char32_t
+      signaling_NaN() noexcept { return char32_t(); }
+
+      static constexpr char32_t
+      denorm_min() noexcept { return char32_t(); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = !is_signed;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style = round_toward_zero;
+    };
+
+
+
+  template<>
+    struct numeric_limits<short>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr short
+      min() noexcept { return -0x7fff - 1; }
+
+      static constexpr short
+      max() noexcept { return 0x7fff; }
+
+
+      static constexpr short
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(short) * 8 - ((short)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(short) * 8 - ((short)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr short
+      epsilon() noexcept { return 0; }
+
+      static constexpr short
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr short
+      infinity() noexcept { return short(); }
+
+      static constexpr short
+      quiet_NaN() noexcept { return short(); }
+
+      static constexpr short
+      signaling_NaN() noexcept { return short(); }
+
+      static constexpr short
+      denorm_min() noexcept { return short(); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<unsigned short>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr unsigned short
+      min() noexcept { return 0; }
+
+      static constexpr unsigned short
+      max() noexcept { return 0x7fff * 2U + 1; }
+
+
+      static constexpr unsigned short
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(unsigned short) * 8 - ((unsigned short)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(unsigned short) * 8 - ((unsigned short)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr unsigned short
+      epsilon() noexcept { return 0; }
+
+      static constexpr unsigned short
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr unsigned short
+      infinity() noexcept
+      { return static_cast<unsigned short>(0); }
+
+      static constexpr unsigned short
+      quiet_NaN() noexcept
+      { return static_cast<unsigned short>(0); }
+
+      static constexpr unsigned short
+      signaling_NaN() noexcept
+      { return static_cast<unsigned short>(0); }
+
+      static constexpr unsigned short
+      denorm_min() noexcept
+      { return static_cast<unsigned short>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = true;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<int>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr int
+      min() noexcept { return -0x7fffffff - 1; }
+
+      static constexpr int
+      max() noexcept { return 0x7fffffff; }
+
+
+      static constexpr int
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(int) * 8 - ((int)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(int) * 8 - ((int)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr int
+      epsilon() noexcept { return 0; }
+
+      static constexpr int
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr int
+      infinity() noexcept { return static_cast<int>(0); }
+
+      static constexpr int
+      quiet_NaN() noexcept { return static_cast<int>(0); }
+
+      static constexpr int
+      signaling_NaN() noexcept { return static_cast<int>(0); }
+
+      static constexpr int
+      denorm_min() noexcept { return static_cast<int>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<unsigned int>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr unsigned int
+      min() noexcept { return 0; }
+
+      static constexpr unsigned int
+      max() noexcept { return 0x7fffffff * 2U + 1; }
+
+
+      static constexpr unsigned int
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(unsigned int) * 8 - ((unsigned int)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(unsigned int) * 8 - ((unsigned int)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr unsigned int
+      epsilon() noexcept { return 0; }
+
+      static constexpr unsigned int
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr unsigned int
+      infinity() noexcept { return static_cast<unsigned int>(0); }
+
+      static constexpr unsigned int
+      quiet_NaN() noexcept
+      { return static_cast<unsigned int>(0); }
+
+      static constexpr unsigned int
+      signaling_NaN() noexcept
+      { return static_cast<unsigned int>(0); }
+
+      static constexpr unsigned int
+      denorm_min() noexcept
+      { return static_cast<unsigned int>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = true;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<long>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr long
+      min() noexcept { return -0x7fffffffffffffffL - 1; }
+
+      static constexpr long
+      max() noexcept { return 0x7fffffffffffffffL; }
+
+
+      static constexpr long
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits = (sizeof(long) * 8 - ((long)(-1) < 0));
+      static constexpr int digits10 = ((sizeof(long) * 8 - ((long)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr long
+      epsilon() noexcept { return 0; }
+
+      static constexpr long
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr long
+      infinity() noexcept { return static_cast<long>(0); }
+
+      static constexpr long
+      quiet_NaN() noexcept { return static_cast<long>(0); }
+
+      static constexpr long
+      signaling_NaN() noexcept { return static_cast<long>(0); }
+
+      static constexpr long
+      denorm_min() noexcept { return static_cast<long>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<unsigned long>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr unsigned long
+      min() noexcept { return 0; }
+
+      static constexpr unsigned long
+      max() noexcept { return 0x7fffffffffffffffL * 2UL + 1; }
+
+
+      static constexpr unsigned long
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(unsigned long) * 8 - ((unsigned long)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(unsigned long) * 8 - ((unsigned long)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr unsigned long
+      epsilon() noexcept { return 0; }
+
+      static constexpr unsigned long
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr unsigned long
+      infinity() noexcept
+      { return static_cast<unsigned long>(0); }
+
+      static constexpr unsigned long
+      quiet_NaN() noexcept
+      { return static_cast<unsigned long>(0); }
+
+      static constexpr unsigned long
+      signaling_NaN() noexcept
+      { return static_cast<unsigned long>(0); }
+
+      static constexpr unsigned long
+      denorm_min() noexcept
+      { return static_cast<unsigned long>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = true;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<long long>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr long long
+      min() noexcept { return -0x7fffffffffffffffLL - 1; }
+
+      static constexpr long long
+      max() noexcept { return 0x7fffffffffffffffLL; }
+
+
+      static constexpr long long
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(long long) * 8 - ((long long)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(long long) * 8 - ((long long)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr long long
+      epsilon() noexcept { return 0; }
+
+      static constexpr long long
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr long long
+      infinity() noexcept { return static_cast<long long>(0); }
+
+      static constexpr long long
+      quiet_NaN() noexcept { return static_cast<long long>(0); }
+
+      static constexpr long long
+      signaling_NaN() noexcept
+      { return static_cast<long long>(0); }
+
+      static constexpr long long
+      denorm_min() noexcept { return static_cast<long long>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+
+
+  template<>
+    struct numeric_limits<unsigned long long>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr unsigned long long
+      min() noexcept { return 0; }
+
+      static constexpr unsigned long long
+      max() noexcept { return 0x7fffffffffffffffLL * 2ULL + 1; }
+
+
+      static constexpr unsigned long long
+      lowest() noexcept { return min(); }
+
+
+      static constexpr int digits
+       = (sizeof(unsigned long long) * 8 - ((unsigned long long)(-1) < 0));
+      static constexpr int digits10
+       = ((sizeof(unsigned long long) * 8 - ((unsigned long long)(-1) < 0)) * 643L / 2136);
+
+      static constexpr int max_digits10 = 0;
+
+      static constexpr bool is_signed = false;
+      static constexpr bool is_integer = true;
+      static constexpr bool is_exact = true;
+      static constexpr int radix = 2;
+
+      static constexpr unsigned long long
+      epsilon() noexcept { return 0; }
+
+      static constexpr unsigned long long
+      round_error() noexcept { return 0; }
+
+      static constexpr int min_exponent = 0;
+      static constexpr int min_exponent10 = 0;
+      static constexpr int max_exponent = 0;
+      static constexpr int max_exponent10 = 0;
+
+      static constexpr bool has_infinity = false;
+      static constexpr bool has_quiet_NaN = false;
+      static constexpr bool has_signaling_NaN = false;
+      static constexpr float_denorm_style has_denorm
+       = denorm_absent;
+      static constexpr bool has_denorm_loss = false;
+
+      static constexpr unsigned long long
+      infinity() noexcept
+      { return static_cast<unsigned long long>(0); }
+
+      static constexpr unsigned long long
+      quiet_NaN() noexcept
+      { return static_cast<unsigned long long>(0); }
+
+      static constexpr unsigned long long
+      signaling_NaN() noexcept
+      { return static_cast<unsigned long long>(0); }
+
+      static constexpr unsigned long long
+      denorm_min() noexcept
+      { return static_cast<unsigned long long>(0); }
+
+      static constexpr bool is_iec559 = false;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = true;
+
+      static constexpr bool traps = true;
+      static constexpr bool tinyness_before = false;
+      static constexpr float_round_style round_style
+       = round_toward_zero;
+    };
+# 1637 "/usr/include/c++/13/limits" 3
+  __extension__ template<> struct numeric_limits<__int128> { static constexpr bool is_specialized = true; static constexpr __int128 min() noexcept { return (((__int128)(-1) < 0) ? -(((__int128)(-1) < 0) ? (((((__int128)1 << ((128 - ((__int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(__int128)0) - 1 : (__int128)0); } static constexpr __int128 max() noexcept { return (((__int128)(-1) < 0) ? (((((__int128)1 << ((128 - ((__int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(__int128)0); } static constexpr int digits = 128 - 1; static constexpr int digits10 = (128 - 1) * 643L / 2136; static constexpr bool is_signed = true; static constexpr bool is_integer = true; static constexpr bool is_exact = true; static constexpr int radix = 2; static constexpr __int128 epsilon() noexcept { return 0; } static constexpr __int128 round_error() noexcept { return 0; } static constexpr __int128 lowest() noexcept { return min(); } static constexpr int max_digits10 = 0; static constexpr int min_exponent = 0; static constexpr int min_exponent10 = 0; static constexpr int max_exponent = 0; static constexpr int max_exponent10 = 0; static constexpr bool has_infinity = false; static constexpr bool has_quiet_NaN = false; static constexpr bool has_signaling_NaN = false; static constexpr float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = false; static constexpr __int128 infinity() noexcept { return static_cast<__int128>(0); } static constexpr __int128 quiet_NaN() noexcept { return static_cast<__int128>(0); } static constexpr __int128 signaling_NaN() noexcept { return static_cast<__int128>(0); } static constexpr __int128 denorm_min() noexcept { return static_cast<__int128>(0); } static constexpr bool is_iec559 = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = false; static constexpr bool traps = true; static constexpr bool tinyness_before = false; static constexpr float_round_style round_style = round_toward_zero; }; __extension__ template<> struct numeric_limits<unsigned __int128> { static constexpr bool is_specialized = true; static constexpr unsigned __int128 min() noexcept { return 0; } static constexpr unsigned __int128 max() noexcept { return (((unsigned __int128)(-1) < 0) ? (((((unsigned __int128)1 << ((128 - ((unsigned __int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(unsigned __int128)0); } static constexpr unsigned __int128 lowest() noexcept { return min(); } static constexpr int max_digits10 = 0; static constexpr int digits = 128; static constexpr int digits10 = 128 * 643L / 2136; static constexpr bool is_signed = false; static constexpr bool is_integer = true; static constexpr bool is_exact = true; static constexpr int radix = 2; static constexpr unsigned __int128 epsilon() noexcept { return 0; } static constexpr unsigned __int128 round_error() noexcept { return 0; } static constexpr int min_exponent = 0; static constexpr int min_exponent10 = 0; static constexpr int max_exponent = 0; static constexpr int max_exponent10 = 0; static constexpr bool has_infinity = false; static constexpr bool has_quiet_NaN = false; static constexpr bool has_signaling_NaN = false; static constexpr float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = false; static constexpr unsigned __int128 infinity() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 quiet_NaN() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 signaling_NaN() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 denorm_min() noexcept { return static_cast<unsigned __int128>(0); } static constexpr bool is_iec559 = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = true; static constexpr bool traps = true; static constexpr bool tinyness_before = false; static constexpr float_round_style round_style = round_toward_zero; };
+# 1669 "/usr/include/c++/13/limits" 3
+  template<>
+    struct numeric_limits<float>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr float
+      min() noexcept { return 1.17549435082228750796873653722224568e-38F; }
+
+      static constexpr float
+      max() noexcept { return 3.40282346638528859811704183484516925e+38F; }
+
+
+      static constexpr float
+      lowest() noexcept { return -3.40282346638528859811704183484516925e+38F; }
+
+
+      static constexpr int digits = 24;
+      static constexpr int digits10 = 6;
+
+      static constexpr int max_digits10
+  = (2 + (24) * 643L / 2136);
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = false;
+      static constexpr bool is_exact = false;
+      static constexpr int radix = 2;
+
+      static constexpr float
+      epsilon() noexcept { return 1.19209289550781250000000000000000000e-7F; }
+
+      static constexpr float
+      round_error() noexcept { return 0.5F; }
+
+      static constexpr int min_exponent = (-125);
+      static constexpr int min_exponent10 = (-37);
+      static constexpr int max_exponent = 128;
+      static constexpr int max_exponent10 = 38;
+
+      static constexpr bool has_infinity = 1;
+      static constexpr bool has_quiet_NaN = 1;
+      static constexpr bool has_signaling_NaN = has_quiet_NaN;
+      static constexpr float_denorm_style has_denorm
+ = bool(1) ? denorm_present : denorm_absent;
+      static constexpr bool has_denorm_loss
+       = false;
+
+      static constexpr float
+      infinity() noexcept { return __builtin_huge_valf(); }
+
+      static constexpr float
+      quiet_NaN() noexcept { return __builtin_nanf(""); }
+
+      static constexpr float
+      signaling_NaN() noexcept { return __builtin_nansf(""); }
+
+      static constexpr float
+      denorm_min() noexcept { return 1.40129846432481707092372958328991613e-45F; }
+
+      static constexpr bool is_iec559
+ = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = false;
+      static constexpr bool tinyness_before
+       = false;
+      static constexpr float_round_style round_style
+       = round_to_nearest;
+    };
+
+
+
+
+
+
+  template<>
+    struct numeric_limits<double>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr double
+      min() noexcept { return double(2.22507385850720138309023271733240406e-308L); }
+
+      static constexpr double
+      max() noexcept { return double(1.79769313486231570814527423731704357e+308L); }
+
+
+      static constexpr double
+      lowest() noexcept { return -double(1.79769313486231570814527423731704357e+308L); }
+
+
+      static constexpr int digits = 53;
+      static constexpr int digits10 = 15;
+
+      static constexpr int max_digits10
+  = (2 + (53) * 643L / 2136);
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = false;
+      static constexpr bool is_exact = false;
+      static constexpr int radix = 2;
+
+      static constexpr double
+      epsilon() noexcept { return double(2.22044604925031308084726333618164062e-16L); }
+
+      static constexpr double
+      round_error() noexcept { return 0.5; }
+
+      static constexpr int min_exponent = (-1021);
+      static constexpr int min_exponent10 = (-307);
+      static constexpr int max_exponent = 1024;
+      static constexpr int max_exponent10 = 308;
+
+      static constexpr bool has_infinity = 1;
+      static constexpr bool has_quiet_NaN = 1;
+      static constexpr bool has_signaling_NaN = has_quiet_NaN;
+      static constexpr float_denorm_style has_denorm
+ = bool(1) ? denorm_present : denorm_absent;
+      static constexpr bool has_denorm_loss
+        = false;
+
+      static constexpr double
+      infinity() noexcept { return __builtin_huge_val(); }
+
+      static constexpr double
+      quiet_NaN() noexcept { return __builtin_nan(""); }
+
+      static constexpr double
+      signaling_NaN() noexcept { return __builtin_nans(""); }
+
+      static constexpr double
+      denorm_min() noexcept { return double(4.94065645841246544176568792868221372e-324L); }
+
+      static constexpr bool is_iec559
+ = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = false;
+      static constexpr bool tinyness_before
+       = false;
+      static constexpr float_round_style round_style
+       = round_to_nearest;
+    };
+
+
+
+
+
+
+  template<>
+    struct numeric_limits<long double>
+    {
+      static constexpr bool is_specialized = true;
+
+      static constexpr long double
+      min() noexcept { return 3.36210314311209350626267781732175260e-4932L; }
+
+      static constexpr long double
+      max() noexcept { return 1.18973149535723176508575932662800702e+4932L; }
+
+
+      static constexpr long double
+      lowest() noexcept { return -1.18973149535723176508575932662800702e+4932L; }
+
+
+      static constexpr int digits = 113;
+      static constexpr int digits10 = 33;
+
+      static constexpr int max_digits10
+  = (2 + (113) * 643L / 2136);
+
+      static constexpr bool is_signed = true;
+      static constexpr bool is_integer = false;
+      static constexpr bool is_exact = false;
+      static constexpr int radix = 2;
+
+      static constexpr long double
+      epsilon() noexcept { return 1.92592994438723585305597794258492732e-34L; }
+
+      static constexpr long double
+      round_error() noexcept { return 0.5L; }
+
+      static constexpr int min_exponent = (-16381);
+      static constexpr int min_exponent10 = (-4931);
+      static constexpr int max_exponent = 16384;
+      static constexpr int max_exponent10 = 4932;
+
+      static constexpr bool has_infinity = 1;
+      static constexpr bool has_quiet_NaN = 1;
+      static constexpr bool has_signaling_NaN = has_quiet_NaN;
+      static constexpr float_denorm_style has_denorm
+ = bool(1) ? denorm_present : denorm_absent;
+      static constexpr bool has_denorm_loss
+ = false;
+
+      static constexpr long double
+      infinity() noexcept { return __builtin_huge_vall(); }
+
+      static constexpr long double
+      quiet_NaN() noexcept { return __builtin_nanl(""); }
+
+      static constexpr long double
+      signaling_NaN() noexcept { return __builtin_nansl(""); }
+
+      static constexpr long double
+      denorm_min() noexcept { return 6.47517511943802511092443895822764655e-4966L; }
+
+      static constexpr bool is_iec559
+ = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static constexpr bool is_bounded = true;
+      static constexpr bool is_modulo = false;
+
+      static constexpr bool traps = false;
+      static constexpr bool tinyness_before =
+      false;
+      static constexpr float_round_style round_style =
+            round_to_nearest;
+    };
+# 2076 "/usr/include/c++/13/limits" 3
+
+}
+# 45 "/usr/include/c++/13/bits/specfun.h" 2 3
+
+
+# 1 "/usr/include/c++/13/tr1/gamma.tcc" 1 3
+# 49 "/usr/include/c++/13/tr1/gamma.tcc" 3
+# 1 "/usr/include/c++/13/tr1/special_function_util.h" 1 3
+# 39 "/usr/include/c++/13/tr1/special_function_util.h" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 50 "/usr/include/c++/13/tr1/special_function_util.h" 3
+  namespace __detail
+  {
+
+
+
+    template<typename _Tp>
+    struct __floating_point_constant
+    {
+      static const _Tp __value;
+    };
+
+
+
+    template<typename _Tp>
+      struct __numeric_constants
+      {
+
+        static _Tp __pi() throw()
+        { return static_cast<_Tp>(3.1415926535897932384626433832795029L); }
+
+        static _Tp __pi_2() throw()
+        { return static_cast<_Tp>(1.5707963267948966192313216916397514L); }
+
+        static _Tp __pi_3() throw()
+        { return static_cast<_Tp>(1.0471975511965977461542144610931676L); }
+
+        static _Tp __pi_4() throw()
+        { return static_cast<_Tp>(0.7853981633974483096156608458198757L); }
+
+        static _Tp __1_pi() throw()
+        { return static_cast<_Tp>(0.3183098861837906715377675267450287L); }
+
+        static _Tp __2_sqrtpi() throw()
+        { return static_cast<_Tp>(1.1283791670955125738961589031215452L); }
+
+        static _Tp __sqrt2() throw()
+        { return static_cast<_Tp>(1.4142135623730950488016887242096981L); }
+
+        static _Tp __sqrt3() throw()
+        { return static_cast<_Tp>(1.7320508075688772935274463415058723L); }
+
+        static _Tp __sqrtpio2() throw()
+        { return static_cast<_Tp>(1.2533141373155002512078826424055226L); }
+
+        static _Tp __sqrt1_2() throw()
+        { return static_cast<_Tp>(0.7071067811865475244008443621048490L); }
+
+        static _Tp __lnpi() throw()
+        { return static_cast<_Tp>(1.1447298858494001741434273513530587L); }
+
+        static _Tp __gamma_e() throw()
+        { return static_cast<_Tp>(0.5772156649015328606065120900824024L); }
+
+        static _Tp __euler() throw()
+        { return static_cast<_Tp>(2.7182818284590452353602874713526625L); }
+      };
+# 114 "/usr/include/c++/13/tr1/special_function_util.h" 3
+    template<typename _Tp>
+    inline bool __isnan(_Tp __x)
+    { return std::isnan(__x); }
+# 133 "/usr/include/c++/13/tr1/special_function_util.h" 3
+  }
+
+
+
+
+
+}
+# 50 "/usr/include/c++/13/tr1/gamma.tcc" 2 3
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 65 "/usr/include/c++/13/tr1/gamma.tcc" 3
+  namespace __detail
+  {
+# 76 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template <typename _Tp>
+    _Tp
+    __bernoulli_series(unsigned int __n)
+    {
+
+      static const _Tp __num[28] = {
+        _Tp(1UL), -_Tp(1UL) / _Tp(2UL),
+        _Tp(1UL) / _Tp(6UL), _Tp(0UL),
+        -_Tp(1UL) / _Tp(30UL), _Tp(0UL),
+        _Tp(1UL) / _Tp(42UL), _Tp(0UL),
+        -_Tp(1UL) / _Tp(30UL), _Tp(0UL),
+        _Tp(5UL) / _Tp(66UL), _Tp(0UL),
+        -_Tp(691UL) / _Tp(2730UL), _Tp(0UL),
+        _Tp(7UL) / _Tp(6UL), _Tp(0UL),
+        -_Tp(3617UL) / _Tp(510UL), _Tp(0UL),
+        _Tp(43867UL) / _Tp(798UL), _Tp(0UL),
+        -_Tp(174611) / _Tp(330UL), _Tp(0UL),
+        _Tp(854513UL) / _Tp(138UL), _Tp(0UL),
+        -_Tp(236364091UL) / _Tp(2730UL), _Tp(0UL),
+        _Tp(8553103UL) / _Tp(6UL), _Tp(0UL)
+      };
+
+      if (__n == 0)
+        return _Tp(1);
+
+      if (__n == 1)
+        return -_Tp(1) / _Tp(2);
+
+
+      if (__n % 2 == 1)
+        return _Tp(0);
+
+
+      if (__n < 28)
+        return __num[__n];
+
+
+      _Tp __fact = _Tp(1);
+      if ((__n / 2) % 2 == 0)
+        __fact *= _Tp(-1);
+      for (unsigned int __k = 1; __k <= __n; ++__k)
+        __fact *= __k / (_Tp(2) * __numeric_constants<_Tp>::__pi());
+      __fact *= _Tp(2);
+
+      _Tp __sum = _Tp(0);
+      for (unsigned int __i = 1; __i < 1000; ++__i)
+        {
+          _Tp __term = std::pow(_Tp(__i), -_Tp(__n));
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __sum += __term;
+        }
+
+      return __fact * __sum;
+    }
+# 139 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __bernoulli(int __n)
+    { return __bernoulli_series<_Tp>(__n); }
+# 153 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __log_gamma_bernoulli(_Tp __x)
+    {
+      _Tp __lg = (__x - _Tp(0.5L)) * std::log(__x) - __x
+               + _Tp(0.5L) * std::log(_Tp(2)
+               * __numeric_constants<_Tp>::__pi());
+
+      const _Tp __xx = __x * __x;
+      _Tp __help = _Tp(1) / __x;
+      for ( unsigned int __i = 1; __i < 20; ++__i )
+        {
+          const _Tp __2i = _Tp(2 * __i);
+          __help /= __2i * (__2i - _Tp(1)) * __xx;
+          __lg += __bernoulli<_Tp>(2 * __i) * __help;
+        }
+
+      return __lg;
+    }
+# 181 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __log_gamma_lanczos(_Tp __x)
+    {
+      const _Tp __xm1 = __x - _Tp(1);
+
+      static const _Tp __lanczos_cheb_7[9] = {
+       _Tp( 0.99999999999980993227684700473478L),
+       _Tp( 676.520368121885098567009190444019L),
+       _Tp(-1259.13921672240287047156078755283L),
+       _Tp( 771.3234287776530788486528258894L),
+       _Tp(-176.61502916214059906584551354L),
+       _Tp( 12.507343278686904814458936853L),
+       _Tp(-0.13857109526572011689554707L),
+       _Tp( 9.984369578019570859563e-6L),
+       _Tp( 1.50563273514931155834e-7L)
+      };
+
+      static const _Tp __LOGROOT2PI
+          = _Tp(0.9189385332046727417803297364056176L);
+
+      _Tp __sum = __lanczos_cheb_7[0];
+      for(unsigned int __k = 1; __k < 9; ++__k)
+        __sum += __lanczos_cheb_7[__k] / (__xm1 + __k);
+
+      const _Tp __term1 = (__xm1 + _Tp(0.5L))
+                        * std::log((__xm1 + _Tp(7.5L))
+                       / __numeric_constants<_Tp>::__euler());
+      const _Tp __term2 = __LOGROOT2PI + std::log(__sum);
+      const _Tp __result = __term1 + (__term2 - _Tp(7));
+
+      return __result;
+    }
+# 225 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __log_gamma(_Tp __x)
+    {
+      if (__x > _Tp(0.5L))
+        return __log_gamma_lanczos(__x);
+      else
+        {
+          const _Tp __sin_fact
+                 = std::abs(std::sin(__numeric_constants<_Tp>::__pi() * __x));
+          if (__sin_fact == _Tp(0))
+            std::__throw_domain_error(("Argument is nonpositive integer " "in __log_gamma")
+                                                           );
+          return __numeric_constants<_Tp>::__lnpi()
+                     - std::log(__sin_fact)
+                     - __log_gamma_lanczos(_Tp(1) - __x);
+        }
+    }
+# 252 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __log_gamma_sign(_Tp __x)
+    {
+      if (__x > _Tp(0))
+        return _Tp(1);
+      else
+        {
+          const _Tp __sin_fact
+                  = std::sin(__numeric_constants<_Tp>::__pi() * __x);
+          if (__sin_fact > _Tp(0))
+            return (1);
+          else if (__sin_fact < _Tp(0))
+            return -_Tp(1);
+          else
+            return _Tp(0);
+        }
+    }
+# 283 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __log_bincoef(unsigned int __n, unsigned int __k)
+    {
+
+      static const _Tp __max_bincoeff
+                      = std::numeric_limits<_Tp>::max_exponent10
+                      * std::log(_Tp(10)) - _Tp(1);
+
+      _Tp __coeff = ::std::lgamma(_Tp(1 + __n))
+                  - ::std::lgamma(_Tp(1 + __k))
+                  - ::std::lgamma(_Tp(1 + __n - __k));
+
+
+
+
+
+    }
+# 314 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __bincoef(unsigned int __n, unsigned int __k)
+    {
+
+      static const _Tp __max_bincoeff
+                      = std::numeric_limits<_Tp>::max_exponent10
+                      * std::log(_Tp(10)) - _Tp(1);
+
+      const _Tp __log_coeff = __log_bincoef<_Tp>(__n, __k);
+      if (__log_coeff > __max_bincoeff)
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        return std::exp(__log_coeff);
+    }
+# 337 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __gamma(_Tp __x)
+    { return std::exp(__log_gamma(__x)); }
+# 356 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __psi_series(_Tp __x)
+    {
+      _Tp __sum = -__numeric_constants<_Tp>::__gamma_e() - _Tp(1) / __x;
+      const unsigned int __max_iter = 100000;
+      for (unsigned int __k = 1; __k < __max_iter; ++__k)
+        {
+          const _Tp __term = __x / (__k * (__k + __x));
+          __sum += __term;
+          if (std::abs(__term / __sum) < std::numeric_limits<_Tp>::epsilon())
+            break;
+        }
+      return __sum;
+    }
+# 386 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __psi_asymp(_Tp __x)
+    {
+      _Tp __sum = std::log(__x) - _Tp(0.5L) / __x;
+      const _Tp __xx = __x * __x;
+      _Tp __xp = __xx;
+      const unsigned int __max_iter = 100;
+      for (unsigned int __k = 1; __k < __max_iter; ++__k)
+        {
+          const _Tp __term = __bernoulli<_Tp>(2 * __k) / (2 * __k * __xp);
+          __sum -= __term;
+          if (std::abs(__term / __sum) < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __xp *= __xx;
+        }
+      return __sum;
+    }
+# 417 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __psi(_Tp __x)
+    {
+      const int __n = static_cast<int>(__x + 0.5L);
+      const _Tp __eps = _Tp(4) * std::numeric_limits<_Tp>::epsilon();
+      if (__n <= 0 && std::abs(__x - _Tp(__n)) < __eps)
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x < _Tp(0))
+        {
+          const _Tp __pi = __numeric_constants<_Tp>::__pi();
+          return __psi(_Tp(1) - __x)
+               - __pi * std::cos(__pi * __x) / std::sin(__pi * __x);
+        }
+      else if (__x > _Tp(100))
+        return __psi_asymp(__x);
+      else
+        return __psi_series(__x);
+    }
+# 446 "/usr/include/c++/13/tr1/gamma.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __psi(unsigned int __n, _Tp __x)
+    {
+      if (__x <= _Tp(0))
+        std::__throw_domain_error(("Argument out of range " "in __psi")
+                                                 );
+      else if (__n == 0)
+        return __psi(__x);
+      else
+        {
+          const _Tp __hzeta = __hurwitz_zeta(_Tp(__n + 1), __x);
+
+          const _Tp __ln_nfact = ::std::lgamma(_Tp(__n + 1));
+
+
+
+          _Tp __result = std::exp(__ln_nfact) * __hzeta;
+          if (__n % 2 == 1)
+            __result = -__result;
+          return __result;
+        }
+    }
+  }
+
+
+
+
+
+
+}
+# 48 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/bessel_function.tcc" 1 3
+# 55 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 71 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+  namespace __detail
+  {
+# 98 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    void
+    __gamma_temme(_Tp __mu,
+                  _Tp & __gam1, _Tp & __gam2, _Tp & __gampl, _Tp & __gammi)
+    {
+
+      __gampl = _Tp(1) / ::std::tgamma(_Tp(1) + __mu);
+      __gammi = _Tp(1) / ::std::tgamma(_Tp(1) - __mu);
+
+
+
+
+
+      if (std::abs(__mu) < std::numeric_limits<_Tp>::epsilon())
+        __gam1 = -_Tp(__numeric_constants<_Tp>::__gamma_e());
+      else
+        __gam1 = (__gammi - __gampl) / (_Tp(2) * __mu);
+
+      __gam2 = (__gammi + __gampl) / (_Tp(2));
+
+      return;
+    }
+# 136 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    void
+    __bessel_jn(_Tp __nu, _Tp __x,
+                _Tp & __Jnu, _Tp & __Nnu, _Tp & __Jpnu, _Tp & __Npnu)
+    {
+      if (__x == _Tp(0))
+        {
+          if (__nu == _Tp(0))
+            {
+              __Jnu = _Tp(1);
+              __Jpnu = _Tp(0);
+            }
+          else if (__nu == _Tp(1))
+            {
+              __Jnu = _Tp(0);
+              __Jpnu = _Tp(0.5L);
+            }
+          else
+            {
+              __Jnu = _Tp(0);
+              __Jpnu = _Tp(0);
+            }
+          __Nnu = -std::numeric_limits<_Tp>::infinity();
+          __Npnu = std::numeric_limits<_Tp>::infinity();
+          return;
+        }
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+
+
+
+      const _Tp __fp_min = std::sqrt(std::numeric_limits<_Tp>::min());
+      const int __max_iter = 15000;
+      const _Tp __x_min = _Tp(2);
+
+      const int __nl = (__x < __x_min
+                    ? static_cast<int>(__nu + _Tp(0.5L))
+                    : std::max(0, static_cast<int>(__nu - __x + _Tp(1.5L))));
+
+      const _Tp __mu = __nu - __nl;
+      const _Tp __mu2 = __mu * __mu;
+      const _Tp __xi = _Tp(1) / __x;
+      const _Tp __xi2 = _Tp(2) * __xi;
+      _Tp __w = __xi2 / __numeric_constants<_Tp>::__pi();
+      int __isign = 1;
+      _Tp __h = __nu * __xi;
+      if (__h < __fp_min)
+        __h = __fp_min;
+      _Tp __b = __xi2 * __nu;
+      _Tp __d = _Tp(0);
+      _Tp __c = __h;
+      int __i;
+      for (__i = 1; __i <= __max_iter; ++__i)
+        {
+          __b += __xi2;
+          __d = __b - __d;
+          if (std::abs(__d) < __fp_min)
+            __d = __fp_min;
+          __c = __b - _Tp(1) / __c;
+          if (std::abs(__c) < __fp_min)
+            __c = __fp_min;
+          __d = _Tp(1) / __d;
+          const _Tp __del = __c * __d;
+          __h *= __del;
+          if (__d < _Tp(0))
+            __isign = -__isign;
+          if (std::abs(__del - _Tp(1)) < __eps)
+            break;
+        }
+      if (__i > __max_iter)
+        std::__throw_runtime_error(("Argument x too large in __bessel_jn; " "try asymptotic expansion.")
+                                                                   );
+      _Tp __Jnul = __isign * __fp_min;
+      _Tp __Jpnul = __h * __Jnul;
+      _Tp __Jnul1 = __Jnul;
+      _Tp __Jpnu1 = __Jpnul;
+      _Tp __fact = __nu * __xi;
+      for ( int __l = __nl; __l >= 1; --__l )
+        {
+          const _Tp __Jnutemp = __fact * __Jnul + __Jpnul;
+          __fact -= __xi;
+          __Jpnul = __fact * __Jnutemp - __Jnul;
+          __Jnul = __Jnutemp;
+        }
+      if (__Jnul == _Tp(0))
+        __Jnul = __eps;
+      _Tp __f= __Jpnul / __Jnul;
+      _Tp __Nmu, __Nnu1, __Npmu, __Jmu;
+      if (__x < __x_min)
+        {
+          const _Tp __x2 = __x / _Tp(2);
+          const _Tp __pimu = __numeric_constants<_Tp>::__pi() * __mu;
+          _Tp __fact = (std::abs(__pimu) < __eps
+                      ? _Tp(1) : __pimu / std::sin(__pimu));
+          _Tp __d = -std::log(__x2);
+          _Tp __e = __mu * __d;
+          _Tp __fact2 = (std::abs(__e) < __eps
+                       ? _Tp(1) : std::sinh(__e) / __e);
+          _Tp __gam1, __gam2, __gampl, __gammi;
+          __gamma_temme(__mu, __gam1, __gam2, __gampl, __gammi);
+          _Tp __ff = (_Tp(2) / __numeric_constants<_Tp>::__pi())
+                   * __fact * (__gam1 * std::cosh(__e) + __gam2 * __fact2 * __d);
+          __e = std::exp(__e);
+          _Tp __p = __e / (__numeric_constants<_Tp>::__pi() * __gampl);
+          _Tp __q = _Tp(1) / (__e * __numeric_constants<_Tp>::__pi() * __gammi);
+          const _Tp __pimu2 = __pimu / _Tp(2);
+          _Tp __fact3 = (std::abs(__pimu2) < __eps
+                       ? _Tp(1) : std::sin(__pimu2) / __pimu2 );
+          _Tp __r = __numeric_constants<_Tp>::__pi() * __pimu2 * __fact3 * __fact3;
+          _Tp __c = _Tp(1);
+          __d = -__x2 * __x2;
+          _Tp __sum = __ff + __r * __q;
+          _Tp __sum1 = __p;
+          for (__i = 1; __i <= __max_iter; ++__i)
+            {
+              __ff = (__i * __ff + __p + __q) / (__i * __i - __mu2);
+              __c *= __d / _Tp(__i);
+              __p /= _Tp(__i) - __mu;
+              __q /= _Tp(__i) + __mu;
+              const _Tp __del = __c * (__ff + __r * __q);
+              __sum += __del;
+              const _Tp __del1 = __c * __p - __i * __del;
+              __sum1 += __del1;
+              if ( std::abs(__del) < __eps * (_Tp(1) + std::abs(__sum)) )
+                break;
+            }
+          if ( __i > __max_iter )
+            std::__throw_runtime_error(("Bessel y series failed to converge " "in __bessel_jn.")
+                                                             );
+          __Nmu = -__sum;
+          __Nnu1 = -__sum1 * __xi2;
+          __Npmu = __mu * __xi * __Nmu - __Nnu1;
+          __Jmu = __w / (__Npmu - __f * __Nmu);
+        }
+      else
+        {
+          _Tp __a = _Tp(0.25L) - __mu2;
+          _Tp __q = _Tp(1);
+          _Tp __p = -__xi / _Tp(2);
+          _Tp __br = _Tp(2) * __x;
+          _Tp __bi = _Tp(2);
+          _Tp __fact = __a * __xi / (__p * __p + __q * __q);
+          _Tp __cr = __br + __q * __fact;
+          _Tp __ci = __bi + __p * __fact;
+          _Tp __den = __br * __br + __bi * __bi;
+          _Tp __dr = __br / __den;
+          _Tp __di = -__bi / __den;
+          _Tp __dlr = __cr * __dr - __ci * __di;
+          _Tp __dli = __cr * __di + __ci * __dr;
+          _Tp __temp = __p * __dlr - __q * __dli;
+          __q = __p * __dli + __q * __dlr;
+          __p = __temp;
+          int __i;
+          for (__i = 2; __i <= __max_iter; ++__i)
+            {
+              __a += _Tp(2 * (__i - 1));
+              __bi += _Tp(2);
+              __dr = __a * __dr + __br;
+              __di = __a * __di + __bi;
+              if (std::abs(__dr) + std::abs(__di) < __fp_min)
+                __dr = __fp_min;
+              __fact = __a / (__cr * __cr + __ci * __ci);
+              __cr = __br + __cr * __fact;
+              __ci = __bi - __ci * __fact;
+              if (std::abs(__cr) + std::abs(__ci) < __fp_min)
+                __cr = __fp_min;
+              __den = __dr * __dr + __di * __di;
+              __dr /= __den;
+              __di /= -__den;
+              __dlr = __cr * __dr - __ci * __di;
+              __dli = __cr * __di + __ci * __dr;
+              __temp = __p * __dlr - __q * __dli;
+              __q = __p * __dli + __q * __dlr;
+              __p = __temp;
+              if (std::abs(__dlr - _Tp(1)) + std::abs(__dli) < __eps)
+                break;
+          }
+          if (__i > __max_iter)
+            std::__throw_runtime_error(("Lentz's method failed " "in __bessel_jn.")
+                                                             );
+          const _Tp __gam = (__p - __f) / __q;
+          __Jmu = std::sqrt(__w / ((__p - __f) * __gam + __q));
+
+          __Jmu = ::std::copysign(__Jmu, __Jnul);
+
+
+
+
+          __Nmu = __gam * __Jmu;
+          __Npmu = (__p + __q / __gam) * __Nmu;
+          __Nnu1 = __mu * __xi * __Nmu - __Npmu;
+      }
+      __fact = __Jmu / __Jnul;
+      __Jnu = __fact * __Jnul1;
+      __Jpnu = __fact * __Jpnu1;
+      for (__i = 1; __i <= __nl; ++__i)
+        {
+          const _Tp __Nnutemp = (__mu + __i) * __xi2 * __Nnu1 - __Nmu;
+          __Nmu = __Nnu1;
+          __Nnu1 = __Nnutemp;
+        }
+      __Nnu = __Nmu;
+      __Npnu = __nu * __xi * __Nmu - __Nnu1;
+
+      return;
+    }
+# 361 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    void
+    __cyl_bessel_jn_asymp(_Tp __nu, _Tp __x, _Tp & __Jnu, _Tp & __Nnu)
+    {
+      const _Tp __mu = _Tp(4) * __nu * __nu;
+      const _Tp __8x = _Tp(8) * __x;
+
+      _Tp __P = _Tp(0);
+      _Tp __Q = _Tp(0);
+
+      _Tp __k = _Tp(0);
+      _Tp __term = _Tp(1);
+
+      int __epsP = 0;
+      int __epsQ = 0;
+
+      _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+      do
+        {
+          __term *= (__k == 0
+                     ? _Tp(1)
+                     : -(__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x));
+
+          __epsP = std::abs(__term) < __eps * std::abs(__P);
+          __P += __term;
+
+          __k++;
+
+          __term *= (__mu - (2 * __k - 1) * (2 * __k - 1)) / (__k * __8x);
+          __epsQ = std::abs(__term) < __eps * std::abs(__Q);
+          __Q += __term;
+
+          if (__epsP && __epsQ && __k > (__nu / 2.))
+            break;
+
+          __k++;
+        }
+      while (__k < 1000);
+
+      const _Tp __chi = __x - (__nu + _Tp(0.5L))
+                             * __numeric_constants<_Tp>::__pi_2();
+
+      const _Tp __c = std::cos(__chi);
+      const _Tp __s = std::sin(__chi);
+
+      const _Tp __coef = std::sqrt(_Tp(2)
+                             / (__numeric_constants<_Tp>::__pi() * __x));
+
+      __Jnu = __coef * (__c * __P - __s * __Q);
+      __Nnu = __coef * (__s * __P + __c * __Q);
+
+      return;
+    }
+# 444 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    _Tp
+    __cyl_bessel_ij_series(_Tp __nu, _Tp __x, _Tp __sgn,
+                           unsigned int __max_iter)
+    {
+      if (__x == _Tp(0))
+ return __nu == _Tp(0) ? _Tp(1) : _Tp(0);
+
+      const _Tp __x2 = __x / _Tp(2);
+      _Tp __fact = __nu * std::log(__x2);
+
+      __fact -= ::std::lgamma(__nu + _Tp(1));
+
+
+
+      __fact = std::exp(__fact);
+      const _Tp __xx4 = __sgn * __x2 * __x2;
+      _Tp __Jn = _Tp(1);
+      _Tp __term = _Tp(1);
+
+      for (unsigned int __i = 1; __i < __max_iter; ++__i)
+        {
+          __term *= __xx4 / (_Tp(__i) * (__nu + _Tp(__i)));
+          __Jn += __term;
+          if (std::abs(__term / __Jn) < std::numeric_limits<_Tp>::epsilon())
+            break;
+        }
+
+      return __fact * __Jn;
+    }
+# 490 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __cyl_bessel_j(_Tp __nu, _Tp __x)
+    {
+      if (__nu < _Tp(0) || __x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __cyl_bessel_j.")
+                                                           );
+      else if (__isnan(__nu) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x * __x < _Tp(10) * (__nu + _Tp(1)))
+        return __cyl_bessel_ij_series(__nu, __x, -_Tp(1), 200);
+      else if (__x > _Tp(1000))
+        {
+          _Tp __J_nu, __N_nu;
+          __cyl_bessel_jn_asymp(__nu, __x, __J_nu, __N_nu);
+          return __J_nu;
+        }
+      else
+        {
+          _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
+          __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
+          return __J_nu;
+        }
+    }
+# 532 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __cyl_neumann_n(_Tp __nu, _Tp __x)
+    {
+      if (__nu < _Tp(0) || __x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __cyl_neumann_n.")
+                                                            );
+      else if (__isnan(__nu) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x > _Tp(1000))
+        {
+          _Tp __J_nu, __N_nu;
+          __cyl_bessel_jn_asymp(__nu, __x, __J_nu, __N_nu);
+          return __N_nu;
+        }
+      else
+        {
+          _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
+          __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
+          return __N_nu;
+        }
+    }
+# 569 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    void
+    __sph_bessel_jn(unsigned int __n, _Tp __x,
+                    _Tp & __j_n, _Tp & __n_n, _Tp & __jp_n, _Tp & __np_n)
+    {
+      const _Tp __nu = _Tp(__n) + _Tp(0.5L);
+
+      _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
+      __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
+
+      const _Tp __factor = __numeric_constants<_Tp>::__sqrtpio2()
+                         / std::sqrt(__x);
+
+      __j_n = __factor * __J_nu;
+      __n_n = __factor * __N_nu;
+      __jp_n = __factor * __Jp_nu - __j_n / (_Tp(2) * __x);
+      __np_n = __factor * __Np_nu - __n_n / (_Tp(2) * __x);
+
+      return;
+    }
+# 604 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    _Tp
+    __sph_bessel(unsigned int __n, _Tp __x)
+    {
+      if (__x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __sph_bessel.")
+                                                         );
+      else if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x == _Tp(0))
+        {
+          if (__n == 0)
+            return _Tp(1);
+          else
+            return _Tp(0);
+        }
+      else
+        {
+          _Tp __j_n, __n_n, __jp_n, __np_n;
+          __sph_bessel_jn(__n, __x, __j_n, __n_n, __jp_n, __np_n);
+          return __j_n;
+        }
+    }
+# 642 "/usr/include/c++/13/tr1/bessel_function.tcc" 3
+    template <typename _Tp>
+    _Tp
+    __sph_neumann(unsigned int __n, _Tp __x)
+    {
+      if (__x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __sph_neumann.")
+                                                          );
+      else if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x == _Tp(0))
+        return -std::numeric_limits<_Tp>::infinity();
+      else
+        {
+          _Tp __j_n, __n_n, __jp_n, __np_n;
+          __sph_bessel_jn(__n, __x, __j_n, __n_n, __jp_n, __np_n);
+          return __n_n;
+        }
+    }
+  }
+
+
+
+
+
+
+}
+# 49 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/beta_function.tcc" 1 3
+# 49 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 65 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+  namespace __detail
+  {
+# 79 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __beta_gamma(_Tp __x, _Tp __y)
+    {
+
+      _Tp __bet;
+
+      if (__x > __y)
+        {
+          __bet = ::std::tgamma(__x)
+                / ::std::tgamma(__x + __y);
+          __bet *= ::std::tgamma(__y);
+        }
+      else
+        {
+          __bet = ::std::tgamma(__y)
+                / ::std::tgamma(__x + __y);
+          __bet *= ::std::tgamma(__x);
+        }
+# 111 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+      return __bet;
+    }
+# 127 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __beta_lgamma(_Tp __x, _Tp __y)
+    {
+
+      _Tp __bet = ::std::lgamma(__x)
+                + ::std::lgamma(__y)
+                - ::std::lgamma(__x + __y);
+
+
+
+
+
+      __bet = std::exp(__bet);
+      return __bet;
+    }
+# 158 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __beta_product(_Tp __x, _Tp __y)
+    {
+
+      _Tp __bet = (__x + __y) / (__x * __y);
+
+      unsigned int __max_iter = 1000000;
+      for (unsigned int __k = 1; __k < __max_iter; ++__k)
+        {
+          _Tp __term = (_Tp(1) + (__x + __y) / __k)
+                     / ((_Tp(1) + __x / __k) * (_Tp(1) + __y / __k));
+          __bet *= __term;
+        }
+
+      return __bet;
+    }
+# 189 "/usr/include/c++/13/tr1/beta_function.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __beta(_Tp __x, _Tp __y)
+    {
+      if (__isnan(__x) || __isnan(__y))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        return __beta_lgamma(__x, __y);
+    }
+  }
+
+
+
+
+
+
+}
+# 50 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/ell_integral.tcc" 1 3
+# 45 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 59 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+  namespace __detail
+  {
+# 76 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_rf(_Tp __x, _Tp __y, _Tp __z)
+    {
+      const _Tp __min = std::numeric_limits<_Tp>::min();
+      const _Tp __lolim = _Tp(5) * __min;
+
+      if (__x < _Tp(0) || __y < _Tp(0) || __z < _Tp(0))
+        std::__throw_domain_error(("Argument less than zero " "in __ellint_rf.")
+                                                        );
+      else if (__x + __y < __lolim || __x + __z < __lolim
+            || __y + __z < __lolim)
+        std::__throw_domain_error(("Argument too small in __ellint_rf"));
+      else
+        {
+          const _Tp __c0 = _Tp(1) / _Tp(4);
+          const _Tp __c1 = _Tp(1) / _Tp(24);
+          const _Tp __c2 = _Tp(1) / _Tp(10);
+          const _Tp __c3 = _Tp(3) / _Tp(44);
+          const _Tp __c4 = _Tp(1) / _Tp(14);
+
+          _Tp __xn = __x;
+          _Tp __yn = __y;
+          _Tp __zn = __z;
+
+          const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+          const _Tp __errtol = std::pow(__eps, _Tp(1) / _Tp(6));
+          _Tp __mu;
+          _Tp __xndev, __yndev, __zndev;
+
+          const unsigned int __max_iter = 100;
+          for (unsigned int __iter = 0; __iter < __max_iter; ++__iter)
+            {
+              __mu = (__xn + __yn + __zn) / _Tp(3);
+              __xndev = 2 - (__mu + __xn) / __mu;
+              __yndev = 2 - (__mu + __yn) / __mu;
+              __zndev = 2 - (__mu + __zn) / __mu;
+              _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev));
+              __epsilon = std::max(__epsilon, std::abs(__zndev));
+              if (__epsilon < __errtol)
+                break;
+              const _Tp __xnroot = std::sqrt(__xn);
+              const _Tp __ynroot = std::sqrt(__yn);
+              const _Tp __znroot = std::sqrt(__zn);
+              const _Tp __lambda = __xnroot * (__ynroot + __znroot)
+                                 + __ynroot * __znroot;
+              __xn = __c0 * (__xn + __lambda);
+              __yn = __c0 * (__yn + __lambda);
+              __zn = __c0 * (__zn + __lambda);
+            }
+
+          const _Tp __e2 = __xndev * __yndev - __zndev * __zndev;
+          const _Tp __e3 = __xndev * __yndev * __zndev;
+          const _Tp __s = _Tp(1) + (__c1 * __e2 - __c2 - __c3 * __e3) * __e2
+                   + __c4 * __e3;
+
+          return __s / std::sqrt(__mu);
+        }
+    }
+# 153 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __comp_ellint_1_series(_Tp __k)
+    {
+
+      const _Tp __kk = __k * __k;
+
+      _Tp __term = __kk / _Tp(4);
+      _Tp __sum = _Tp(1) + __term;
+
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 2; __i < __max_iter; ++__i)
+        {
+          __term *= (2 * __i - 1) * __kk / (2 * __i);
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __sum += __term;
+        }
+
+      return __numeric_constants<_Tp>::__pi_2() * __sum;
+    }
+# 191 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __comp_ellint_1(_Tp __k)
+    {
+
+      if (__isnan(__k))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (std::abs(__k) >= _Tp(1))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        return __ellint_rf(_Tp(0), _Tp(1) - __k * __k, _Tp(1));
+    }
+# 219 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_1(_Tp __k, _Tp __phi)
+    {
+
+      if (__isnan(__k) || __isnan(__phi))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (std::abs(__k) > _Tp(1))
+        std::__throw_domain_error(("Bad argument in __ellint_1."));
+      else
+        {
+
+          const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi()
+                                   + _Tp(0.5L));
+          const _Tp __phi_red = __phi
+                              - __n * __numeric_constants<_Tp>::__pi();
+
+          const _Tp __s = std::sin(__phi_red);
+          const _Tp __c = std::cos(__phi_red);
+
+          const _Tp __F = __s
+                        * __ellint_rf(__c * __c,
+                                _Tp(1) - __k * __k * __s * __s, _Tp(1));
+
+          if (__n == 0)
+            return __F;
+          else
+            return __F + _Tp(2) * __n * __comp_ellint_1(__k);
+        }
+    }
+# 266 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __comp_ellint_2_series(_Tp __k)
+    {
+
+      const _Tp __kk = __k * __k;
+
+      _Tp __term = __kk;
+      _Tp __sum = __term;
+
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 2; __i < __max_iter; ++__i)
+        {
+          const _Tp __i2m = 2 * __i - 1;
+          const _Tp __i2 = 2 * __i;
+          __term *= __i2m * __i2m * __kk / (__i2 * __i2);
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __sum += __term / __i2m;
+        }
+
+      return __numeric_constants<_Tp>::__pi_2() * (_Tp(1) - __sum);
+    }
+# 314 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_rd(_Tp __x, _Tp __y, _Tp __z)
+    {
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __errtol = std::pow(__eps / _Tp(8), _Tp(1) / _Tp(6));
+      const _Tp __max = std::numeric_limits<_Tp>::max();
+      const _Tp __lolim = _Tp(2) / std::pow(__max, _Tp(2) / _Tp(3));
+
+      if (__x < _Tp(0) || __y < _Tp(0))
+        std::__throw_domain_error(("Argument less than zero " "in __ellint_rd.")
+                                                        );
+      else if (__x + __y < __lolim || __z < __lolim)
+        std::__throw_domain_error(("Argument too small " "in __ellint_rd.")
+                                                        );
+      else
+        {
+          const _Tp __c0 = _Tp(1) / _Tp(4);
+          const _Tp __c1 = _Tp(3) / _Tp(14);
+          const _Tp __c2 = _Tp(1) / _Tp(6);
+          const _Tp __c3 = _Tp(9) / _Tp(22);
+          const _Tp __c4 = _Tp(3) / _Tp(26);
+
+          _Tp __xn = __x;
+          _Tp __yn = __y;
+          _Tp __zn = __z;
+          _Tp __sigma = _Tp(0);
+          _Tp __power4 = _Tp(1);
+
+          _Tp __mu;
+          _Tp __xndev, __yndev, __zndev;
+
+          const unsigned int __max_iter = 100;
+          for (unsigned int __iter = 0; __iter < __max_iter; ++__iter)
+            {
+              __mu = (__xn + __yn + _Tp(3) * __zn) / _Tp(5);
+              __xndev = (__mu - __xn) / __mu;
+              __yndev = (__mu - __yn) / __mu;
+              __zndev = (__mu - __zn) / __mu;
+              _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev));
+              __epsilon = std::max(__epsilon, std::abs(__zndev));
+              if (__epsilon < __errtol)
+                break;
+              _Tp __xnroot = std::sqrt(__xn);
+              _Tp __ynroot = std::sqrt(__yn);
+              _Tp __znroot = std::sqrt(__zn);
+              _Tp __lambda = __xnroot * (__ynroot + __znroot)
+                           + __ynroot * __znroot;
+              __sigma += __power4 / (__znroot * (__zn + __lambda));
+              __power4 *= __c0;
+              __xn = __c0 * (__xn + __lambda);
+              __yn = __c0 * (__yn + __lambda);
+              __zn = __c0 * (__zn + __lambda);
+            }
+
+          _Tp __ea = __xndev * __yndev;
+          _Tp __eb = __zndev * __zndev;
+          _Tp __ec = __ea - __eb;
+          _Tp __ed = __ea - _Tp(6) * __eb;
+          _Tp __ef = __ed + __ec + __ec;
+          _Tp __s1 = __ed * (-__c1 + __c3 * __ed
+                                   / _Tp(3) - _Tp(3) * __c4 * __zndev * __ef
+                                   / _Tp(2));
+          _Tp __s2 = __zndev
+                   * (__c2 * __ef
+                    + __zndev * (-__c3 * __ec - __zndev * __c4 - __ea));
+
+          return _Tp(3) * __sigma + __power4 * (_Tp(1) + __s1 + __s2)
+                                        / (__mu * std::sqrt(__mu));
+        }
+    }
+# 399 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __comp_ellint_2(_Tp __k)
+    {
+
+      if (__isnan(__k))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (std::abs(__k) == 1)
+        return _Tp(1);
+      else if (std::abs(__k) > _Tp(1))
+        std::__throw_domain_error(("Bad argument in __comp_ellint_2."));
+      else
+        {
+          const _Tp __kk = __k * __k;
+
+          return __ellint_rf(_Tp(0), _Tp(1) - __kk, _Tp(1))
+               - __kk * __ellint_rd(_Tp(0), _Tp(1) - __kk, _Tp(1)) / _Tp(3);
+        }
+    }
+# 433 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_2(_Tp __k, _Tp __phi)
+    {
+
+      if (__isnan(__k) || __isnan(__phi))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (std::abs(__k) > _Tp(1))
+        std::__throw_domain_error(("Bad argument in __ellint_2."));
+      else
+        {
+
+          const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi()
+                                   + _Tp(0.5L));
+          const _Tp __phi_red = __phi
+                              - __n * __numeric_constants<_Tp>::__pi();
+
+          const _Tp __kk = __k * __k;
+          const _Tp __s = std::sin(__phi_red);
+          const _Tp __ss = __s * __s;
+          const _Tp __sss = __ss * __s;
+          const _Tp __c = std::cos(__phi_red);
+          const _Tp __cc = __c * __c;
+
+          const _Tp __E = __s
+                        * __ellint_rf(__cc, _Tp(1) - __kk * __ss, _Tp(1))
+                        - __kk * __sss
+                        * __ellint_rd(__cc, _Tp(1) - __kk * __ss, _Tp(1))
+                        / _Tp(3);
+
+          if (__n == 0)
+            return __E;
+          else
+            return __E + _Tp(2) * __n * __comp_ellint_2(__k);
+        }
+    }
+# 492 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_rc(_Tp __x, _Tp __y)
+    {
+      const _Tp __min = std::numeric_limits<_Tp>::min();
+      const _Tp __lolim = _Tp(5) * __min;
+
+      if (__x < _Tp(0) || __y < _Tp(0) || __x + __y < __lolim)
+        std::__throw_domain_error(("Argument less than zero " "in __ellint_rc.")
+                                                        );
+      else
+        {
+          const _Tp __c0 = _Tp(1) / _Tp(4);
+          const _Tp __c1 = _Tp(1) / _Tp(7);
+          const _Tp __c2 = _Tp(9) / _Tp(22);
+          const _Tp __c3 = _Tp(3) / _Tp(10);
+          const _Tp __c4 = _Tp(3) / _Tp(8);
+
+          _Tp __xn = __x;
+          _Tp __yn = __y;
+
+          const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+          const _Tp __errtol = std::pow(__eps / _Tp(30), _Tp(1) / _Tp(6));
+          _Tp __mu;
+          _Tp __sn;
+
+          const unsigned int __max_iter = 100;
+          for (unsigned int __iter = 0; __iter < __max_iter; ++__iter)
+            {
+              __mu = (__xn + _Tp(2) * __yn) / _Tp(3);
+              __sn = (__yn + __mu) / __mu - _Tp(2);
+              if (std::abs(__sn) < __errtol)
+                break;
+              const _Tp __lambda = _Tp(2) * std::sqrt(__xn) * std::sqrt(__yn)
+                             + __yn;
+              __xn = __c0 * (__xn + __lambda);
+              __yn = __c0 * (__yn + __lambda);
+            }
+
+          _Tp __s = __sn * __sn
+                  * (__c3 + __sn*(__c1 + __sn * (__c4 + __sn * __c2)));
+
+          return (_Tp(1) + __s) / std::sqrt(__mu);
+        }
+    }
+# 561 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_rj(_Tp __x, _Tp __y, _Tp __z, _Tp __p)
+    {
+      const _Tp __min = std::numeric_limits<_Tp>::min();
+      const _Tp __lolim = std::pow(_Tp(5) * __min, _Tp(1)/_Tp(3));
+
+      if (__x < _Tp(0) || __y < _Tp(0) || __z < _Tp(0))
+        std::__throw_domain_error(("Argument less than zero " "in __ellint_rj.")
+                                                        );
+      else if (__x + __y < __lolim || __x + __z < __lolim
+            || __y + __z < __lolim || __p < __lolim)
+        std::__throw_domain_error(("Argument too small " "in __ellint_rj")
+                                                       );
+      else
+        {
+          const _Tp __c0 = _Tp(1) / _Tp(4);
+          const _Tp __c1 = _Tp(3) / _Tp(14);
+          const _Tp __c2 = _Tp(1) / _Tp(3);
+          const _Tp __c3 = _Tp(3) / _Tp(22);
+          const _Tp __c4 = _Tp(3) / _Tp(26);
+
+          _Tp __xn = __x;
+          _Tp __yn = __y;
+          _Tp __zn = __z;
+          _Tp __pn = __p;
+          _Tp __sigma = _Tp(0);
+          _Tp __power4 = _Tp(1);
+
+          const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+          const _Tp __errtol = std::pow(__eps / _Tp(8), _Tp(1) / _Tp(6));
+
+          _Tp __mu;
+          _Tp __xndev, __yndev, __zndev, __pndev;
+
+          const unsigned int __max_iter = 100;
+          for (unsigned int __iter = 0; __iter < __max_iter; ++__iter)
+            {
+              __mu = (__xn + __yn + __zn + _Tp(2) * __pn) / _Tp(5);
+              __xndev = (__mu - __xn) / __mu;
+              __yndev = (__mu - __yn) / __mu;
+              __zndev = (__mu - __zn) / __mu;
+              __pndev = (__mu - __pn) / __mu;
+              _Tp __epsilon = std::max(std::abs(__xndev), std::abs(__yndev));
+              __epsilon = std::max(__epsilon, std::abs(__zndev));
+              __epsilon = std::max(__epsilon, std::abs(__pndev));
+              if (__epsilon < __errtol)
+                break;
+              const _Tp __xnroot = std::sqrt(__xn);
+              const _Tp __ynroot = std::sqrt(__yn);
+              const _Tp __znroot = std::sqrt(__zn);
+              const _Tp __lambda = __xnroot * (__ynroot + __znroot)
+                                 + __ynroot * __znroot;
+              const _Tp __alpha1 = __pn * (__xnroot + __ynroot + __znroot)
+                                + __xnroot * __ynroot * __znroot;
+              const _Tp __alpha2 = __alpha1 * __alpha1;
+              const _Tp __beta = __pn * (__pn + __lambda)
+                                      * (__pn + __lambda);
+              __sigma += __power4 * __ellint_rc(__alpha2, __beta);
+              __power4 *= __c0;
+              __xn = __c0 * (__xn + __lambda);
+              __yn = __c0 * (__yn + __lambda);
+              __zn = __c0 * (__zn + __lambda);
+              __pn = __c0 * (__pn + __lambda);
+            }
+
+          _Tp __ea = __xndev * (__yndev + __zndev) + __yndev * __zndev;
+          _Tp __eb = __xndev * __yndev * __zndev;
+          _Tp __ec = __pndev * __pndev;
+          _Tp __e2 = __ea - _Tp(3) * __ec;
+          _Tp __e3 = __eb + _Tp(2) * __pndev * (__ea - __ec);
+          _Tp __s1 = _Tp(1) + __e2 * (-__c1 + _Tp(3) * __c3 * __e2 / _Tp(4)
+                            - _Tp(3) * __c4 * __e3 / _Tp(2));
+          _Tp __s2 = __eb * (__c2 / _Tp(2)
+                   + __pndev * (-__c3 - __c3 + __pndev * __c4));
+          _Tp __s3 = __pndev * __ea * (__c2 - __pndev * __c3)
+                   - __c2 * __pndev * __ec;
+
+          return _Tp(3) * __sigma + __power4 * (__s1 + __s2 + __s3)
+                                             / (__mu * std::sqrt(__mu));
+        }
+    }
+# 661 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __comp_ellint_3(_Tp __k, _Tp __nu)
+    {
+
+      if (__isnan(__k) || __isnan(__nu))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__nu == _Tp(1))
+        return std::numeric_limits<_Tp>::infinity();
+      else if (std::abs(__k) > _Tp(1))
+        std::__throw_domain_error(("Bad argument in __comp_ellint_3."));
+      else
+        {
+          const _Tp __kk = __k * __k;
+
+          return __ellint_rf(_Tp(0), _Tp(1) - __kk, _Tp(1))
+               + __nu
+               * __ellint_rj(_Tp(0), _Tp(1) - __kk, _Tp(1), _Tp(1) - __nu)
+               / _Tp(3);
+        }
+    }
+# 701 "/usr/include/c++/13/tr1/ell_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __ellint_3(_Tp __k, _Tp __nu, _Tp __phi)
+    {
+
+      if (__isnan(__k) || __isnan(__nu) || __isnan(__phi))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (std::abs(__k) > _Tp(1))
+        std::__throw_domain_error(("Bad argument in __ellint_3."));
+      else
+        {
+
+          const int __n = std::floor(__phi / __numeric_constants<_Tp>::__pi()
+                                   + _Tp(0.5L));
+          const _Tp __phi_red = __phi
+                              - __n * __numeric_constants<_Tp>::__pi();
+
+          const _Tp __kk = __k * __k;
+          const _Tp __s = std::sin(__phi_red);
+          const _Tp __ss = __s * __s;
+          const _Tp __sss = __ss * __s;
+          const _Tp __c = std::cos(__phi_red);
+          const _Tp __cc = __c * __c;
+
+          const _Tp __Pi = __s
+                         * __ellint_rf(__cc, _Tp(1) - __kk * __ss, _Tp(1))
+                         + __nu * __sss
+                         * __ellint_rj(__cc, _Tp(1) - __kk * __ss, _Tp(1),
+                                       _Tp(1) - __nu * __ss) / _Tp(3);
+
+          if (__n == 0)
+            return __Pi;
+          else
+            return __Pi + _Tp(2) * __n * __comp_ellint_3(__k, __nu);
+        }
+    }
+  }
+
+
+
+
+
+}
+# 51 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/exp_integral.tcc" 1 3
+# 50 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 64 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+  namespace __detail
+  {
+    template<typename _Tp> _Tp __expint_E1(_Tp);
+# 81 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_E1_series(_Tp __x)
+    {
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      _Tp __term = _Tp(1);
+      _Tp __esum = _Tp(0);
+      _Tp __osum = _Tp(0);
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 1; __i < __max_iter; ++__i)
+        {
+          __term *= - __x / __i;
+          if (std::abs(__term) < __eps)
+            break;
+          if (__term >= _Tp(0))
+            __esum += __term / __i;
+          else
+            __osum += __term / __i;
+        }
+
+      return - __esum - __osum
+             - __numeric_constants<_Tp>::__gamma_e() - std::log(__x);
+    }
+# 118 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_E1_asymp(_Tp __x)
+    {
+      _Tp __term = _Tp(1);
+      _Tp __esum = _Tp(1);
+      _Tp __osum = _Tp(0);
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 1; __i < __max_iter; ++__i)
+        {
+          _Tp __prev = __term;
+          __term *= - __i / __x;
+          if (std::abs(__term) > std::abs(__prev))
+            break;
+          if (__term >= _Tp(0))
+            __esum += __term;
+          else
+            __osum += __term;
+        }
+
+      return std::exp(- __x) * (__esum + __osum) / __x;
+    }
+# 155 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_En_series(unsigned int __n, _Tp __x)
+    {
+      const unsigned int __max_iter = 1000;
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const int __nm1 = __n - 1;
+      _Tp __ans = (__nm1 != 0
+                ? _Tp(1) / __nm1 : -std::log(__x)
+                                   - __numeric_constants<_Tp>::__gamma_e());
+      _Tp __fact = _Tp(1);
+      for (int __i = 1; __i <= __max_iter; ++__i)
+        {
+          __fact *= -__x / _Tp(__i);
+          _Tp __del;
+          if ( __i != __nm1 )
+            __del = -__fact / _Tp(__i - __nm1);
+          else
+            {
+              _Tp __psi = -__numeric_constants<_Tp>::gamma_e();
+              for (int __ii = 1; __ii <= __nm1; ++__ii)
+                __psi += _Tp(1) / _Tp(__ii);
+              __del = __fact * (__psi - std::log(__x));
+            }
+          __ans += __del;
+          if (std::abs(__del) < __eps * std::abs(__ans))
+            return __ans;
+        }
+      std::__throw_runtime_error(("Series summation failed " "in __expint_En_series.")
+                                                              );
+    }
+# 201 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_En_cont_frac(unsigned int __n, _Tp __x)
+    {
+      const unsigned int __max_iter = 1000;
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __fp_min = std::numeric_limits<_Tp>::min();
+      const int __nm1 = __n - 1;
+      _Tp __b = __x + _Tp(__n);
+      _Tp __c = _Tp(1) / __fp_min;
+      _Tp __d = _Tp(1) / __b;
+      _Tp __h = __d;
+      for ( unsigned int __i = 1; __i <= __max_iter; ++__i )
+        {
+          _Tp __a = -_Tp(__i * (__nm1 + __i));
+          __b += _Tp(2);
+          __d = _Tp(1) / (__a * __d + __b);
+          __c = __b + __a / __c;
+          const _Tp __del = __c * __d;
+          __h *= __del;
+          if (std::abs(__del - _Tp(1)) < __eps)
+            {
+              const _Tp __ans = __h * std::exp(-__x);
+              return __ans;
+            }
+        }
+      std::__throw_runtime_error(("Continued fraction failed " "in __expint_En_cont_frac.")
+                                                                 );
+    }
+# 246 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_En_recursion(unsigned int __n, _Tp __x)
+    {
+      _Tp __En;
+      _Tp __E1 = __expint_E1(__x);
+      if (__x < _Tp(__n))
+        {
+
+          __En = __E1;
+          for (unsigned int __j = 2; __j < __n; ++__j)
+            __En = (std::exp(-__x) - __x * __En) / _Tp(__j - 1);
+        }
+      else
+        {
+
+          __En = _Tp(1);
+          const int __N = __n + 20;
+          _Tp __save = _Tp(0);
+          for (int __j = __N; __j > 0; --__j)
+            {
+              __En = (std::exp(-__x) - __j * __En) / __x;
+              if (__j == __n)
+                __save = __En;
+            }
+            _Tp __norm = __En / __E1;
+            __En /= __norm;
+        }
+
+      return __En;
+    }
+# 290 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_Ei_series(_Tp __x)
+    {
+      _Tp __term = _Tp(1);
+      _Tp __sum = _Tp(0);
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 1; __i < __max_iter; ++__i)
+        {
+          __term *= __x / __i;
+          __sum += __term / __i;
+          if (__term < std::numeric_limits<_Tp>::epsilon() * __sum)
+            break;
+        }
+
+      return __numeric_constants<_Tp>::__gamma_e() + __sum + std::log(__x);
+    }
+# 321 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_Ei_asymp(_Tp __x)
+    {
+      _Tp __term = _Tp(1);
+      _Tp __sum = _Tp(1);
+      const unsigned int __max_iter = 1000;
+      for (unsigned int __i = 1; __i < __max_iter; ++__i)
+        {
+          _Tp __prev = __term;
+          __term *= __i / __x;
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            break;
+          if (__term >= __prev)
+            break;
+          __sum += __term;
+        }
+
+      return std::exp(__x) * __sum / __x;
+    }
+# 354 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_Ei(_Tp __x)
+    {
+      if (__x < _Tp(0))
+        return -__expint_E1(-__x);
+      else if (__x < -std::log(std::numeric_limits<_Tp>::epsilon()))
+        return __expint_Ei_series(__x);
+      else
+        return __expint_Ei_asymp(__x);
+    }
+# 378 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_E1(_Tp __x)
+    {
+      if (__x < _Tp(0))
+        return -__expint_Ei(-__x);
+      else if (__x < _Tp(1))
+        return __expint_E1_series(__x);
+      else if (__x < _Tp(100))
+        return __expint_En_cont_frac(1, __x);
+      else
+        return __expint_E1_asymp(__x);
+    }
+# 408 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_asymp(unsigned int __n, _Tp __x)
+    {
+      _Tp __term = _Tp(1);
+      _Tp __sum = _Tp(1);
+      for (unsigned int __i = 1; __i <= __n; ++__i)
+        {
+          _Tp __prev = __term;
+          __term *= -(__n - __i + 1) / __x;
+          if (std::abs(__term) > std::abs(__prev))
+            break;
+          __sum += __term;
+        }
+
+      return std::exp(-__x) * __sum / __x;
+    }
+# 442 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint_large_n(unsigned int __n, _Tp __x)
+    {
+      const _Tp __xpn = __x + __n;
+      const _Tp __xpn2 = __xpn * __xpn;
+      _Tp __term = _Tp(1);
+      _Tp __sum = _Tp(1);
+      for (unsigned int __i = 1; __i <= __n; ++__i)
+        {
+          _Tp __prev = __term;
+          __term *= (__n - 2 * (__i - 1) * __x) / __xpn2;
+          if (std::abs(__term) < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __sum += __term;
+        }
+
+      return std::exp(-__x) * __sum / __xpn;
+    }
+# 476 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __expint(unsigned int __n, _Tp __x)
+    {
+
+      if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__n <= 1 && __x == _Tp(0))
+        return std::numeric_limits<_Tp>::infinity();
+      else
+        {
+          _Tp __E0 = std::exp(__x) / __x;
+          if (__n == 0)
+            return __E0;
+
+          _Tp __E1 = __expint_E1(__x);
+          if (__n == 1)
+            return __E1;
+
+          if (__x == _Tp(0))
+            return _Tp(1) / static_cast<_Tp>(__n - 1);
+
+          _Tp __En = __expint_En_recursion(__n, __x);
+
+          return __En;
+        }
+    }
+# 516 "/usr/include/c++/13/tr1/exp_integral.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __expint(_Tp __x)
+    {
+      if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        return __expint_Ei(__x);
+    }
+  }
+
+
+
+
+
+}
+# 52 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/hypergeometric.tcc" 1 3
+# 44 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 60 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+  namespace __detail
+  {
+# 83 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __conf_hyperg_series(_Tp __a, _Tp __c, _Tp __x)
+    {
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+      _Tp __term = _Tp(1);
+      _Tp __Fac = _Tp(1);
+      const unsigned int __max_iter = 100000;
+      unsigned int __i;
+      for (__i = 0; __i < __max_iter; ++__i)
+        {
+          __term *= (__a + _Tp(__i)) * __x
+                  / ((__c + _Tp(__i)) * _Tp(1 + __i));
+          if (std::abs(__term) < __eps)
+            {
+              break;
+            }
+          __Fac += __term;
+        }
+      if (__i == __max_iter)
+        std::__throw_runtime_error(("Series failed to converge " "in __conf_hyperg_series.")
+                                                                  );
+
+      return __Fac;
+    }
+# 120 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __conf_hyperg_luke(_Tp __a, _Tp __c, _Tp __xin)
+    {
+      const _Tp __big = std::pow(std::numeric_limits<_Tp>::max(), _Tp(0.16L));
+      const int __nmax = 20000;
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __x = -__xin;
+      const _Tp __x3 = __x * __x * __x;
+      const _Tp __t0 = __a / __c;
+      const _Tp __t1 = (__a + _Tp(1)) / (_Tp(2) * __c);
+      const _Tp __t2 = (__a + _Tp(2)) / (_Tp(2) * (__c + _Tp(1)));
+      _Tp __F = _Tp(1);
+      _Tp __prec;
+
+      _Tp __Bnm3 = _Tp(1);
+      _Tp __Bnm2 = _Tp(1) + __t1 * __x;
+      _Tp __Bnm1 = _Tp(1) + __t2 * __x * (_Tp(1) + __t1 / _Tp(3) * __x);
+
+      _Tp __Anm3 = _Tp(1);
+      _Tp __Anm2 = __Bnm2 - __t0 * __x;
+      _Tp __Anm1 = __Bnm1 - __t0 * (_Tp(1) + __t2 * __x) * __x
+                 + __t0 * __t1 * (__c / (__c + _Tp(1))) * __x * __x;
+
+      int __n = 3;
+      while(1)
+        {
+          _Tp __npam1 = _Tp(__n - 1) + __a;
+          _Tp __npcm1 = _Tp(__n - 1) + __c;
+          _Tp __npam2 = _Tp(__n - 2) + __a;
+          _Tp __npcm2 = _Tp(__n - 2) + __c;
+          _Tp __tnm1 = _Tp(2 * __n - 1);
+          _Tp __tnm3 = _Tp(2 * __n - 3);
+          _Tp __tnm5 = _Tp(2 * __n - 5);
+          _Tp __F1 = (_Tp(__n - 2) - __a) / (_Tp(2) * __tnm3 * __npcm1);
+          _Tp __F2 = (_Tp(__n) + __a) * __npam1
+                   / (_Tp(4) * __tnm1 * __tnm3 * __npcm2 * __npcm1);
+          _Tp __F3 = -__npam2 * __npam1 * (_Tp(__n - 2) - __a)
+                   / (_Tp(8) * __tnm3 * __tnm3 * __tnm5
+                   * (_Tp(__n - 3) + __c) * __npcm2 * __npcm1);
+          _Tp __E = -__npam1 * (_Tp(__n - 1) - __c)
+                   / (_Tp(2) * __tnm3 * __npcm2 * __npcm1);
+
+          _Tp __An = (_Tp(1) + __F1 * __x) * __Anm1
+                   + (__E + __F2 * __x) * __x * __Anm2 + __F3 * __x3 * __Anm3;
+          _Tp __Bn = (_Tp(1) + __F1 * __x) * __Bnm1
+                   + (__E + __F2 * __x) * __x * __Bnm2 + __F3 * __x3 * __Bnm3;
+          _Tp __r = __An / __Bn;
+
+          __prec = std::abs((__F - __r) / __F);
+          __F = __r;
+
+          if (__prec < __eps || __n > __nmax)
+            break;
+
+          if (std::abs(__An) > __big || std::abs(__Bn) > __big)
+            {
+              __An /= __big;
+              __Bn /= __big;
+              __Anm1 /= __big;
+              __Bnm1 /= __big;
+              __Anm2 /= __big;
+              __Bnm2 /= __big;
+              __Anm3 /= __big;
+              __Bnm3 /= __big;
+            }
+          else if (std::abs(__An) < _Tp(1) / __big
+                || std::abs(__Bn) < _Tp(1) / __big)
+            {
+              __An *= __big;
+              __Bn *= __big;
+              __Anm1 *= __big;
+              __Bnm1 *= __big;
+              __Anm2 *= __big;
+              __Bnm2 *= __big;
+              __Anm3 *= __big;
+              __Bnm3 *= __big;
+            }
+
+          ++__n;
+          __Bnm3 = __Bnm2;
+          __Bnm2 = __Bnm1;
+          __Bnm1 = __Bn;
+          __Anm3 = __Anm2;
+          __Anm2 = __Anm1;
+          __Anm1 = __An;
+        }
+
+      if (__n >= __nmax)
+        std::__throw_runtime_error(("Iteration failed to converge " "in __conf_hyperg_luke.")
+                                                                );
+
+      return __F;
+    }
+# 227 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __conf_hyperg(_Tp __a, _Tp __c, _Tp __x)
+    {
+
+      const _Tp __c_nint = ::std::nearbyint(__c);
+
+
+
+      if (__isnan(__a) || __isnan(__c) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__c_nint == __c && __c_nint <= 0)
+        return std::numeric_limits<_Tp>::infinity();
+      else if (__a == _Tp(0))
+        return _Tp(1);
+      else if (__c == __a)
+        return std::exp(__x);
+      else if (__x < _Tp(0))
+        return __conf_hyperg_luke(__a, __c, __x);
+      else
+        return __conf_hyperg_series(__a, __c, __x);
+    }
+# 271 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __hyperg_series(_Tp __a, _Tp __b, _Tp __c, _Tp __x)
+    {
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+      _Tp __term = _Tp(1);
+      _Tp __Fabc = _Tp(1);
+      const unsigned int __max_iter = 100000;
+      unsigned int __i;
+      for (__i = 0; __i < __max_iter; ++__i)
+        {
+          __term *= (__a + _Tp(__i)) * (__b + _Tp(__i)) * __x
+                  / ((__c + _Tp(__i)) * _Tp(1 + __i));
+          if (std::abs(__term) < __eps)
+            {
+              break;
+            }
+          __Fabc += __term;
+        }
+      if (__i == __max_iter)
+        std::__throw_runtime_error(("Series failed to converge " "in __hyperg_series.")
+                                                             );
+
+      return __Fabc;
+    }
+
+
+
+
+
+
+
+    template<typename _Tp>
+    _Tp
+    __hyperg_luke(_Tp __a, _Tp __b, _Tp __c, _Tp __xin)
+    {
+      const _Tp __big = std::pow(std::numeric_limits<_Tp>::max(), _Tp(0.16L));
+      const int __nmax = 20000;
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __x = -__xin;
+      const _Tp __x3 = __x * __x * __x;
+      const _Tp __t0 = __a * __b / __c;
+      const _Tp __t1 = (__a + _Tp(1)) * (__b + _Tp(1)) / (_Tp(2) * __c);
+      const _Tp __t2 = (__a + _Tp(2)) * (__b + _Tp(2))
+                     / (_Tp(2) * (__c + _Tp(1)));
+
+      _Tp __F = _Tp(1);
+
+      _Tp __Bnm3 = _Tp(1);
+      _Tp __Bnm2 = _Tp(1) + __t1 * __x;
+      _Tp __Bnm1 = _Tp(1) + __t2 * __x * (_Tp(1) + __t1 / _Tp(3) * __x);
+
+      _Tp __Anm3 = _Tp(1);
+      _Tp __Anm2 = __Bnm2 - __t0 * __x;
+      _Tp __Anm1 = __Bnm1 - __t0 * (_Tp(1) + __t2 * __x) * __x
+                 + __t0 * __t1 * (__c / (__c + _Tp(1))) * __x * __x;
+
+      int __n = 3;
+      while (1)
+        {
+          const _Tp __npam1 = _Tp(__n - 1) + __a;
+          const _Tp __npbm1 = _Tp(__n - 1) + __b;
+          const _Tp __npcm1 = _Tp(__n - 1) + __c;
+          const _Tp __npam2 = _Tp(__n - 2) + __a;
+          const _Tp __npbm2 = _Tp(__n - 2) + __b;
+          const _Tp __npcm2 = _Tp(__n - 2) + __c;
+          const _Tp __tnm1 = _Tp(2 * __n - 1);
+          const _Tp __tnm3 = _Tp(2 * __n - 3);
+          const _Tp __tnm5 = _Tp(2 * __n - 5);
+          const _Tp __n2 = __n * __n;
+          const _Tp __F1 = (_Tp(3) * __n2 + (__a + __b - _Tp(6)) * __n
+                         + _Tp(2) - __a * __b - _Tp(2) * (__a + __b))
+                         / (_Tp(2) * __tnm3 * __npcm1);
+          const _Tp __F2 = -(_Tp(3) * __n2 - (__a + __b + _Tp(6)) * __n
+                         + _Tp(2) - __a * __b) * __npam1 * __npbm1
+                         / (_Tp(4) * __tnm1 * __tnm3 * __npcm2 * __npcm1);
+          const _Tp __F3 = (__npam2 * __npam1 * __npbm2 * __npbm1
+                         * (_Tp(__n - 2) - __a) * (_Tp(__n - 2) - __b))
+                         / (_Tp(8) * __tnm3 * __tnm3 * __tnm5
+                         * (_Tp(__n - 3) + __c) * __npcm2 * __npcm1);
+          const _Tp __E = -__npam1 * __npbm1 * (_Tp(__n - 1) - __c)
+                         / (_Tp(2) * __tnm3 * __npcm2 * __npcm1);
+
+          _Tp __An = (_Tp(1) + __F1 * __x) * __Anm1
+                   + (__E + __F2 * __x) * __x * __Anm2 + __F3 * __x3 * __Anm3;
+          _Tp __Bn = (_Tp(1) + __F1 * __x) * __Bnm1
+                   + (__E + __F2 * __x) * __x * __Bnm2 + __F3 * __x3 * __Bnm3;
+          const _Tp __r = __An / __Bn;
+
+          const _Tp __prec = std::abs((__F - __r) / __F);
+          __F = __r;
+
+          if (__prec < __eps || __n > __nmax)
+            break;
+
+          if (std::abs(__An) > __big || std::abs(__Bn) > __big)
+            {
+              __An /= __big;
+              __Bn /= __big;
+              __Anm1 /= __big;
+              __Bnm1 /= __big;
+              __Anm2 /= __big;
+              __Bnm2 /= __big;
+              __Anm3 /= __big;
+              __Bnm3 /= __big;
+            }
+          else if (std::abs(__An) < _Tp(1) / __big
+                || std::abs(__Bn) < _Tp(1) / __big)
+            {
+              __An *= __big;
+              __Bn *= __big;
+              __Anm1 *= __big;
+              __Bnm1 *= __big;
+              __Anm2 *= __big;
+              __Bnm2 *= __big;
+              __Anm3 *= __big;
+              __Bnm3 *= __big;
+            }
+
+          ++__n;
+          __Bnm3 = __Bnm2;
+          __Bnm2 = __Bnm1;
+          __Bnm1 = __Bn;
+          __Anm3 = __Anm2;
+          __Anm2 = __Anm1;
+          __Anm1 = __An;
+        }
+
+      if (__n >= __nmax)
+        std::__throw_runtime_error(("Iteration failed to converge " "in __hyperg_luke.")
+                                                           );
+
+      return __F;
+    }
+# 438 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __hyperg_reflect(_Tp __a, _Tp __b, _Tp __c, _Tp __x)
+    {
+      const _Tp __d = __c - __a - __b;
+      const int __intd = std::floor(__d + _Tp(0.5L));
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __toler = _Tp(1000) * __eps;
+      const _Tp __log_max = std::log(std::numeric_limits<_Tp>::max());
+      const bool __d_integer = (std::abs(__d - __intd) < __toler);
+
+      if (__d_integer)
+        {
+          const _Tp __ln_omx = std::log(_Tp(1) - __x);
+          const _Tp __ad = std::abs(__d);
+          _Tp __F1, __F2;
+
+          _Tp __d1, __d2;
+          if (__d >= _Tp(0))
+            {
+              __d1 = __d;
+              __d2 = _Tp(0);
+            }
+          else
+            {
+              __d1 = _Tp(0);
+              __d2 = __d;
+            }
+
+          const _Tp __lng_c = __log_gamma(__c);
+
+
+          if (__ad < __eps)
+            {
+
+              __F1 = _Tp(0);
+            }
+          else
+            {
+
+              bool __ok_d1 = true;
+              _Tp __lng_ad, __lng_ad1, __lng_bd1;
+              try
+                {
+                  __lng_ad = __log_gamma(__ad);
+                  __lng_ad1 = __log_gamma(__a + __d1);
+                  __lng_bd1 = __log_gamma(__b + __d1);
+                }
+              catch(...)
+                {
+                  __ok_d1 = false;
+                }
+
+              if (__ok_d1)
+                {
+
+
+
+                  _Tp __sum1 = _Tp(1);
+                  _Tp __term = _Tp(1);
+                  _Tp __ln_pre1 = __lng_ad + __lng_c + __d2 * __ln_omx
+                                - __lng_ad1 - __lng_bd1;
+
+
+
+                  for (int __i = 1; __i < __ad; ++__i)
+                    {
+                      const int __j = __i - 1;
+                      __term *= (__a + __d2 + __j) * (__b + __d2 + __j)
+                              / (_Tp(1) + __d2 + __j) / __i * (_Tp(1) - __x);
+                      __sum1 += __term;
+                    }
+
+                  if (__ln_pre1 > __log_max)
+                    std::__throw_runtime_error(("Overflow of gamma functions" " in __hyperg_luke.")
+                                                                        );
+                  else
+                    __F1 = std::exp(__ln_pre1) * __sum1;
+                }
+              else
+                {
+
+
+                  __F1 = _Tp(0);
+                }
+            }
+
+
+          bool __ok_d2 = true;
+          _Tp __lng_ad2, __lng_bd2;
+          try
+            {
+              __lng_ad2 = __log_gamma(__a + __d2);
+              __lng_bd2 = __log_gamma(__b + __d2);
+            }
+          catch(...)
+            {
+              __ok_d2 = false;
+            }
+
+          if (__ok_d2)
+            {
+
+
+              const int __maxiter = 2000;
+              const _Tp __psi_1 = -__numeric_constants<_Tp>::__gamma_e();
+              const _Tp __psi_1pd = __psi(_Tp(1) + __ad);
+              const _Tp __psi_apd1 = __psi(__a + __d1);
+              const _Tp __psi_bpd1 = __psi(__b + __d1);
+
+              _Tp __psi_term = __psi_1 + __psi_1pd - __psi_apd1
+                             - __psi_bpd1 - __ln_omx;
+              _Tp __fact = _Tp(1);
+              _Tp __sum2 = __psi_term;
+              _Tp __ln_pre2 = __lng_c + __d1 * __ln_omx
+                            - __lng_ad2 - __lng_bd2;
+
+
+              int __j;
+              for (__j = 1; __j < __maxiter; ++__j)
+                {
+
+
+                  const _Tp __term1 = _Tp(1) / _Tp(__j)
+                                    + _Tp(1) / (__ad + __j);
+                  const _Tp __term2 = _Tp(1) / (__a + __d1 + _Tp(__j - 1))
+                                    + _Tp(1) / (__b + __d1 + _Tp(__j - 1));
+                  __psi_term += __term1 - __term2;
+                  __fact *= (__a + __d1 + _Tp(__j - 1))
+                          * (__b + __d1 + _Tp(__j - 1))
+                          / ((__ad + __j) * __j) * (_Tp(1) - __x);
+                  const _Tp __delta = __fact * __psi_term;
+                  __sum2 += __delta;
+                  if (std::abs(__delta) < __eps * std::abs(__sum2))
+                    break;
+                }
+              if (__j == __maxiter)
+                std::__throw_runtime_error(("Sum F2 failed to converge " "in __hyperg_reflect")
+                                                                     );
+
+              if (__sum2 == _Tp(0))
+                __F2 = _Tp(0);
+              else
+                __F2 = std::exp(__ln_pre2) * __sum2;
+            }
+          else
+            {
+
+
+              __F2 = _Tp(0);
+            }
+
+          const _Tp __sgn_2 = (__intd % 2 == 1 ? -_Tp(1) : _Tp(1));
+          const _Tp __F = __F1 + __sgn_2 * __F2;
+
+          return __F;
+        }
+      else
+        {
+
+
+
+
+          bool __ok1 = true;
+          _Tp __sgn_g1ca = _Tp(0), __ln_g1ca = _Tp(0);
+          _Tp __sgn_g1cb = _Tp(0), __ln_g1cb = _Tp(0);
+          try
+            {
+              __sgn_g1ca = __log_gamma_sign(__c - __a);
+              __ln_g1ca = __log_gamma(__c - __a);
+              __sgn_g1cb = __log_gamma_sign(__c - __b);
+              __ln_g1cb = __log_gamma(__c - __b);
+            }
+          catch(...)
+            {
+              __ok1 = false;
+            }
+
+          bool __ok2 = true;
+          _Tp __sgn_g2a = _Tp(0), __ln_g2a = _Tp(0);
+          _Tp __sgn_g2b = _Tp(0), __ln_g2b = _Tp(0);
+          try
+            {
+              __sgn_g2a = __log_gamma_sign(__a);
+              __ln_g2a = __log_gamma(__a);
+              __sgn_g2b = __log_gamma_sign(__b);
+              __ln_g2b = __log_gamma(__b);
+            }
+          catch(...)
+            {
+              __ok2 = false;
+            }
+
+          const _Tp __sgn_gc = __log_gamma_sign(__c);
+          const _Tp __ln_gc = __log_gamma(__c);
+          const _Tp __sgn_gd = __log_gamma_sign(__d);
+          const _Tp __ln_gd = __log_gamma(__d);
+          const _Tp __sgn_gmd = __log_gamma_sign(-__d);
+          const _Tp __ln_gmd = __log_gamma(-__d);
+
+          const _Tp __sgn1 = __sgn_gc * __sgn_gd * __sgn_g1ca * __sgn_g1cb;
+          const _Tp __sgn2 = __sgn_gc * __sgn_gmd * __sgn_g2a * __sgn_g2b;
+
+          _Tp __pre1, __pre2;
+          if (__ok1 && __ok2)
+            {
+              _Tp __ln_pre1 = __ln_gc + __ln_gd - __ln_g1ca - __ln_g1cb;
+              _Tp __ln_pre2 = __ln_gc + __ln_gmd - __ln_g2a - __ln_g2b
+                            + __d * std::log(_Tp(1) - __x);
+              if (__ln_pre1 < __log_max && __ln_pre2 < __log_max)
+                {
+                  __pre1 = std::exp(__ln_pre1);
+                  __pre2 = std::exp(__ln_pre2);
+                  __pre1 *= __sgn1;
+                  __pre2 *= __sgn2;
+                }
+              else
+                {
+                  std::__throw_runtime_error(("Overflow of gamma functions " "in __hyperg_reflect")
+                                                                       );
+                }
+            }
+          else if (__ok1 && !__ok2)
+            {
+              _Tp __ln_pre1 = __ln_gc + __ln_gd - __ln_g1ca - __ln_g1cb;
+              if (__ln_pre1 < __log_max)
+                {
+                  __pre1 = std::exp(__ln_pre1);
+                  __pre1 *= __sgn1;
+                  __pre2 = _Tp(0);
+                }
+              else
+                {
+                  std::__throw_runtime_error(("Overflow of gamma functions " "in __hyperg_reflect")
+                                                                       );
+                }
+            }
+          else if (!__ok1 && __ok2)
+            {
+              _Tp __ln_pre2 = __ln_gc + __ln_gmd - __ln_g2a - __ln_g2b
+                            + __d * std::log(_Tp(1) - __x);
+              if (__ln_pre2 < __log_max)
+                {
+                  __pre1 = _Tp(0);
+                  __pre2 = std::exp(__ln_pre2);
+                  __pre2 *= __sgn2;
+                }
+              else
+                {
+                  std::__throw_runtime_error(("Overflow of gamma functions " "in __hyperg_reflect")
+                                                                       );
+                }
+            }
+          else
+            {
+              __pre1 = _Tp(0);
+              __pre2 = _Tp(0);
+              std::__throw_runtime_error(("Underflow of gamma functions " "in __hyperg_reflect")
+                                                                   );
+            }
+
+          const _Tp __F1 = __hyperg_series(__a, __b, _Tp(1) - __d,
+                                           _Tp(1) - __x);
+          const _Tp __F2 = __hyperg_series(__c - __a, __c - __b, _Tp(1) + __d,
+                                           _Tp(1) - __x);
+
+          const _Tp __F = __pre1 * __F1 + __pre2 * __F2;
+
+          return __F;
+        }
+    }
+# 728 "/usr/include/c++/13/tr1/hypergeometric.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __hyperg(_Tp __a, _Tp __b, _Tp __c, _Tp __x)
+    {
+
+      const _Tp __a_nint = ::std::nearbyint(__a);
+      const _Tp __b_nint = ::std::nearbyint(__b);
+      const _Tp __c_nint = ::std::nearbyint(__c);
+
+
+
+
+
+      const _Tp __toler = _Tp(1000) * std::numeric_limits<_Tp>::epsilon();
+      if (std::abs(__x) >= _Tp(1))
+        std::__throw_domain_error(("Argument outside unit circle " "in __hyperg.")
+                                                     );
+      else if (__isnan(__a) || __isnan(__b)
+            || __isnan(__c) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__c_nint == __c && __c_nint <= _Tp(0))
+        return std::numeric_limits<_Tp>::infinity();
+      else if (std::abs(__c - __b) < __toler || std::abs(__c - __a) < __toler)
+        return std::pow(_Tp(1) - __x, __c - __a - __b);
+      else if (__a >= _Tp(0) && __b >= _Tp(0) && __c >= _Tp(0)
+            && __x >= _Tp(0) && __x < _Tp(0.995L))
+        return __hyperg_series(__a, __b, __c, __x);
+      else if (std::abs(__a) < _Tp(10) && std::abs(__b) < _Tp(10))
+        {
+
+
+          if (__a < _Tp(0) && std::abs(__a - __a_nint) < __toler)
+            return __hyperg_series(__a_nint, __b, __c, __x);
+          else if (__b < _Tp(0) && std::abs(__b - __b_nint) < __toler)
+            return __hyperg_series(__a, __b_nint, __c, __x);
+          else if (__x < -_Tp(0.25L))
+            return __hyperg_luke(__a, __b, __c, __x);
+          else if (__x < _Tp(0.5L))
+            return __hyperg_series(__a, __b, __c, __x);
+          else
+            if (std::abs(__c) > _Tp(10))
+              return __hyperg_series(__a, __b, __c, __x);
+            else
+              return __hyperg_reflect(__a, __b, __c, __x);
+        }
+      else
+        return __hyperg_luke(__a, __b, __c, __x);
+    }
+  }
+
+
+
+
+
+
+}
+# 53 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/legendre_function.tcc" 1 3
+# 49 "/usr/include/c++/13/tr1/legendre_function.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 65 "/usr/include/c++/13/tr1/legendre_function.tcc" 3
+  namespace __detail
+  {
+# 80 "/usr/include/c++/13/tr1/legendre_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __poly_legendre_p(unsigned int __l, _Tp __x)
+    {
+
+      if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x == +_Tp(1))
+        return +_Tp(1);
+      else if (__x == -_Tp(1))
+        return (__l % 2 == 1 ? -_Tp(1) : +_Tp(1));
+      else
+        {
+          _Tp __p_lm2 = _Tp(1);
+          if (__l == 0)
+            return __p_lm2;
+
+          _Tp __p_lm1 = __x;
+          if (__l == 1)
+            return __p_lm1;
+
+          _Tp __p_l = 0;
+          for (unsigned int __ll = 2; __ll <= __l; ++__ll)
+            {
+
+
+              __p_l = _Tp(2) * __x * __p_lm1 - __p_lm2
+                    - (__x * __p_lm1 - __p_lm2) / _Tp(__ll);
+              __p_lm2 = __p_lm1;
+              __p_lm1 = __p_l;
+            }
+
+          return __p_l;
+        }
+    }
+# 136 "/usr/include/c++/13/tr1/legendre_function.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __assoc_legendre_p(unsigned int __l, unsigned int __m, _Tp __x,
+         _Tp __phase = _Tp(+1))
+    {
+
+      if (__m > __l)
+        return _Tp(0);
+      else if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__m == 0)
+        return __poly_legendre_p(__l, __x);
+      else
+        {
+          _Tp __p_mm = _Tp(1);
+          if (__m > 0)
+            {
+
+
+              _Tp __root = std::sqrt(_Tp(1) - __x) * std::sqrt(_Tp(1) + __x);
+              _Tp __fact = _Tp(1);
+              for (unsigned int __i = 1; __i <= __m; ++__i)
+                {
+                  __p_mm *= __phase * __fact * __root;
+                  __fact += _Tp(2);
+                }
+            }
+          if (__l == __m)
+            return __p_mm;
+
+          _Tp __p_mp1m = _Tp(2 * __m + 1) * __x * __p_mm;
+          if (__l == __m + 1)
+            return __p_mp1m;
+
+          _Tp __p_lm2m = __p_mm;
+          _Tp __P_lm1m = __p_mp1m;
+          _Tp __p_lm = _Tp(0);
+          for (unsigned int __j = __m + 2; __j <= __l; ++__j)
+            {
+              __p_lm = (_Tp(2 * __j - 1) * __x * __P_lm1m
+                      - _Tp(__j + __m - 1) * __p_lm2m) / _Tp(__j - __m);
+              __p_lm2m = __P_lm1m;
+              __P_lm1m = __p_lm;
+            }
+
+          return __p_lm;
+        }
+    }
+# 214 "/usr/include/c++/13/tr1/legendre_function.tcc" 3
+    template <typename _Tp>
+    _Tp
+    __sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
+    {
+      if (__isnan(__theta))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+
+      const _Tp __x = std::cos(__theta);
+
+      if (__m > __l)
+        return _Tp(0);
+      else if (__m == 0)
+        {
+          _Tp __P = __poly_legendre_p(__l, __x);
+          _Tp __fact = std::sqrt(_Tp(2 * __l + 1)
+                     / (_Tp(4) * __numeric_constants<_Tp>::__pi()));
+          __P *= __fact;
+          return __P;
+        }
+      else if (__x == _Tp(1) || __x == -_Tp(1))
+        {
+
+          return _Tp(0);
+        }
+      else
+        {
+
+
+
+
+
+          const _Tp __sgn = ( __m % 2 == 1 ? -_Tp(1) : _Tp(1));
+          const _Tp __y_mp1m_factor = __x * std::sqrt(_Tp(2 * __m + 3));
+
+          const _Tp __lncirc = ::std::log1p(-__x * __x);
+
+
+
+
+
+          const _Tp __lnpoch = ::std::lgamma(_Tp(__m + _Tp(0.5L)))
+                             - ::std::lgamma(_Tp(__m));
+
+
+
+
+          const _Tp __lnpre_val =
+                    -_Tp(0.25L) * __numeric_constants<_Tp>::__lnpi()
+                    + _Tp(0.5L) * (__lnpoch + __m * __lncirc);
+          const _Tp __sr = std::sqrt((_Tp(2) + _Tp(1) / __m)
+                         / (_Tp(4) * __numeric_constants<_Tp>::__pi()));
+          _Tp __y_mm = __sgn * __sr * std::exp(__lnpre_val);
+          _Tp __y_mp1m = __y_mp1m_factor * __y_mm;
+
+          if (__l == __m)
+            return __y_mm;
+          else if (__l == __m + 1)
+            return __y_mp1m;
+          else
+            {
+              _Tp __y_lm = _Tp(0);
+
+
+              for (unsigned int __ll = __m + 2; __ll <= __l; ++__ll)
+                {
+                  const _Tp __rat1 = _Tp(__ll - __m) / _Tp(__ll + __m);
+                  const _Tp __rat2 = _Tp(__ll - __m - 1) / _Tp(__ll + __m - 1);
+                  const _Tp __fact1 = std::sqrt(__rat1 * _Tp(2 * __ll + 1)
+                                                       * _Tp(2 * __ll - 1));
+                  const _Tp __fact2 = std::sqrt(__rat1 * __rat2 * _Tp(2 * __ll + 1)
+                                                                / _Tp(2 * __ll - 3));
+                  __y_lm = (__x * __y_mp1m * __fact1
+                         - (__ll + __m - 1) * __y_mm * __fact2) / _Tp(__ll - __m);
+                  __y_mm = __y_mp1m;
+                  __y_mp1m = __y_lm;
+                }
+
+              return __y_lm;
+            }
+        }
+    }
+  }
+
+
+
+
+
+
+}
+# 54 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 1 3
+# 51 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 65 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+  namespace __detail
+  {
+# 83 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+    template <typename _Tp>
+    void
+    __bessel_ik(_Tp __nu, _Tp __x,
+                _Tp & __Inu, _Tp & __Knu, _Tp & __Ipnu, _Tp & __Kpnu)
+    {
+      if (__x == _Tp(0))
+        {
+          if (__nu == _Tp(0))
+            {
+              __Inu = _Tp(1);
+              __Ipnu = _Tp(0);
+            }
+          else if (__nu == _Tp(1))
+            {
+              __Inu = _Tp(0);
+              __Ipnu = _Tp(0.5L);
+            }
+          else
+            {
+              __Inu = _Tp(0);
+              __Ipnu = _Tp(0);
+            }
+          __Knu = std::numeric_limits<_Tp>::infinity();
+          __Kpnu = -std::numeric_limits<_Tp>::infinity();
+          return;
+        }
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+      const _Tp __fp_min = _Tp(10) * std::numeric_limits<_Tp>::epsilon();
+      const int __max_iter = 15000;
+      const _Tp __x_min = _Tp(2);
+
+      const int __nl = static_cast<int>(__nu + _Tp(0.5L));
+
+      const _Tp __mu = __nu - __nl;
+      const _Tp __mu2 = __mu * __mu;
+      const _Tp __xi = _Tp(1) / __x;
+      const _Tp __xi2 = _Tp(2) * __xi;
+      _Tp __h = __nu * __xi;
+      if ( __h < __fp_min )
+        __h = __fp_min;
+      _Tp __b = __xi2 * __nu;
+      _Tp __d = _Tp(0);
+      _Tp __c = __h;
+      int __i;
+      for ( __i = 1; __i <= __max_iter; ++__i )
+        {
+          __b += __xi2;
+          __d = _Tp(1) / (__b + __d);
+          __c = __b + _Tp(1) / __c;
+          const _Tp __del = __c * __d;
+          __h *= __del;
+          if (std::abs(__del - _Tp(1)) < __eps)
+            break;
+        }
+      if (__i > __max_iter)
+        std::__throw_runtime_error(("Argument x too large " "in __bessel_ik; " "try asymptotic expansion.")
+
+                                                                   );
+      _Tp __Inul = __fp_min;
+      _Tp __Ipnul = __h * __Inul;
+      _Tp __Inul1 = __Inul;
+      _Tp __Ipnu1 = __Ipnul;
+      _Tp __fact = __nu * __xi;
+      for (int __l = __nl; __l >= 1; --__l)
+        {
+          const _Tp __Inutemp = __fact * __Inul + __Ipnul;
+          __fact -= __xi;
+          __Ipnul = __fact * __Inutemp + __Inul;
+          __Inul = __Inutemp;
+        }
+      _Tp __f = __Ipnul / __Inul;
+      _Tp __Kmu, __Knu1;
+      if (__x < __x_min)
+        {
+          const _Tp __x2 = __x / _Tp(2);
+          const _Tp __pimu = __numeric_constants<_Tp>::__pi() * __mu;
+          const _Tp __fact = (std::abs(__pimu) < __eps
+                            ? _Tp(1) : __pimu / std::sin(__pimu));
+          _Tp __d = -std::log(__x2);
+          _Tp __e = __mu * __d;
+          const _Tp __fact2 = (std::abs(__e) < __eps
+                            ? _Tp(1) : std::sinh(__e) / __e);
+          _Tp __gam1, __gam2, __gampl, __gammi;
+          __gamma_temme(__mu, __gam1, __gam2, __gampl, __gammi);
+          _Tp __ff = __fact
+                   * (__gam1 * std::cosh(__e) + __gam2 * __fact2 * __d);
+          _Tp __sum = __ff;
+          __e = std::exp(__e);
+          _Tp __p = __e / (_Tp(2) * __gampl);
+          _Tp __q = _Tp(1) / (_Tp(2) * __e * __gammi);
+          _Tp __c = _Tp(1);
+          __d = __x2 * __x2;
+          _Tp __sum1 = __p;
+          int __i;
+          for (__i = 1; __i <= __max_iter; ++__i)
+            {
+              __ff = (__i * __ff + __p + __q) / (__i * __i - __mu2);
+              __c *= __d / __i;
+              __p /= __i - __mu;
+              __q /= __i + __mu;
+              const _Tp __del = __c * __ff;
+              __sum += __del;
+              const _Tp __del1 = __c * (__p - __i * __ff);
+              __sum1 += __del1;
+              if (std::abs(__del) < __eps * std::abs(__sum))
+                break;
+            }
+          if (__i > __max_iter)
+            std::__throw_runtime_error(("Bessel k series failed to converge " "in __bessel_ik.")
+                                                             );
+          __Kmu = __sum;
+          __Knu1 = __sum1 * __xi2;
+        }
+      else
+        {
+          _Tp __b = _Tp(2) * (_Tp(1) + __x);
+          _Tp __d = _Tp(1) / __b;
+          _Tp __delh = __d;
+          _Tp __h = __delh;
+          _Tp __q1 = _Tp(0);
+          _Tp __q2 = _Tp(1);
+          _Tp __a1 = _Tp(0.25L) - __mu2;
+          _Tp __q = __c = __a1;
+          _Tp __a = -__a1;
+          _Tp __s = _Tp(1) + __q * __delh;
+          int __i;
+          for (__i = 2; __i <= __max_iter; ++__i)
+            {
+              __a -= 2 * (__i - 1);
+              __c = -__a * __c / __i;
+              const _Tp __qnew = (__q1 - __b * __q2) / __a;
+              __q1 = __q2;
+              __q2 = __qnew;
+              __q += __c * __qnew;
+              __b += _Tp(2);
+              __d = _Tp(1) / (__b + __a * __d);
+              __delh = (__b * __d - _Tp(1)) * __delh;
+              __h += __delh;
+              const _Tp __dels = __q * __delh;
+              __s += __dels;
+              if ( std::abs(__dels / __s) < __eps )
+                break;
+            }
+          if (__i > __max_iter)
+            std::__throw_runtime_error(("Steed's method failed " "in __bessel_ik.")
+                                                             );
+          __h = __a1 * __h;
+          __Kmu = std::sqrt(__numeric_constants<_Tp>::__pi() / (_Tp(2) * __x))
+                * std::exp(-__x) / __s;
+          __Knu1 = __Kmu * (__mu + __x + _Tp(0.5L) - __h) * __xi;
+        }
+
+      _Tp __Kpmu = __mu * __xi * __Kmu - __Knu1;
+      _Tp __Inumu = __xi / (__f * __Kmu - __Kpmu);
+      __Inu = __Inumu * __Inul1 / __Inul;
+      __Ipnu = __Inumu * __Ipnu1 / __Inul;
+      for ( __i = 1; __i <= __nl; ++__i )
+        {
+          const _Tp __Knutemp = (__mu + __i) * __xi2 * __Knu1 + __Kmu;
+          __Kmu = __Knu1;
+          __Knu1 = __Knutemp;
+        }
+      __Knu = __Kmu;
+      __Kpnu = __nu * __xi * __Kmu - __Knu1;
+
+      return;
+    }
+# 267 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __cyl_bessel_i(_Tp __nu, _Tp __x)
+    {
+      if (__nu < _Tp(0) || __x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __cyl_bessel_i.")
+                                                           );
+      else if (__isnan(__nu) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__x * __x < _Tp(10) * (__nu + _Tp(1)))
+        return __cyl_bessel_ij_series(__nu, __x, +_Tp(1), 200);
+      else
+        {
+          _Tp __I_nu, __K_nu, __Ip_nu, __Kp_nu;
+          __bessel_ik(__nu, __x, __I_nu, __K_nu, __Ip_nu, __Kp_nu);
+          return __I_nu;
+        }
+    }
+# 303 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __cyl_bessel_k(_Tp __nu, _Tp __x)
+    {
+      if (__nu < _Tp(0) || __x < _Tp(0))
+        std::__throw_domain_error(("Bad argument " "in __cyl_bessel_k.")
+                                                           );
+      else if (__isnan(__nu) || __isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        {
+          _Tp __I_nu, __K_nu, __Ip_nu, __Kp_nu;
+          __bessel_ik(__nu, __x, __I_nu, __K_nu, __Ip_nu, __Kp_nu);
+          return __K_nu;
+        }
+    }
+# 337 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+    template <typename _Tp>
+    void
+    __sph_bessel_ik(unsigned int __n, _Tp __x,
+                    _Tp & __i_n, _Tp & __k_n, _Tp & __ip_n, _Tp & __kp_n)
+    {
+      const _Tp __nu = _Tp(__n) + _Tp(0.5L);
+
+      _Tp __I_nu, __Ip_nu, __K_nu, __Kp_nu;
+      __bessel_ik(__nu, __x, __I_nu, __K_nu, __Ip_nu, __Kp_nu);
+
+      const _Tp __factor = __numeric_constants<_Tp>::__sqrtpio2()
+                         / std::sqrt(__x);
+
+      __i_n = __factor * __I_nu;
+      __k_n = __factor * __K_nu;
+      __ip_n = __factor * __Ip_nu - __i_n / (_Tp(2) * __x);
+      __kp_n = __factor * __Kp_nu - __k_n / (_Tp(2) * __x);
+
+      return;
+    }
+# 373 "/usr/include/c++/13/tr1/modified_bessel_func.tcc" 3
+    template <typename _Tp>
+    void
+    __airy(_Tp __x, _Tp & __Ai, _Tp & __Bi, _Tp & __Aip, _Tp & __Bip)
+    {
+      const _Tp __absx = std::abs(__x);
+      const _Tp __rootx = std::sqrt(__absx);
+      const _Tp __z = _Tp(2) * __absx * __rootx / _Tp(3);
+      const _Tp _S_inf = std::numeric_limits<_Tp>::infinity();
+
+      if (__isnan(__x))
+        __Bip = __Aip = __Bi = __Ai = std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__z == _S_inf)
+        {
+   __Aip = __Ai = _Tp(0);
+   __Bip = __Bi = _S_inf;
+ }
+      else if (__z == -_S_inf)
+ __Bip = __Aip = __Bi = __Ai = _Tp(0);
+      else if (__x > _Tp(0))
+        {
+          _Tp __I_nu, __Ip_nu, __K_nu, __Kp_nu;
+
+          __bessel_ik(_Tp(1) / _Tp(3), __z, __I_nu, __K_nu, __Ip_nu, __Kp_nu);
+          __Ai = __rootx * __K_nu
+               / (__numeric_constants<_Tp>::__sqrt3()
+                * __numeric_constants<_Tp>::__pi());
+          __Bi = __rootx * (__K_nu / __numeric_constants<_Tp>::__pi()
+                 + _Tp(2) * __I_nu / __numeric_constants<_Tp>::__sqrt3());
+
+          __bessel_ik(_Tp(2) / _Tp(3), __z, __I_nu, __K_nu, __Ip_nu, __Kp_nu);
+          __Aip = -__x * __K_nu
+                / (__numeric_constants<_Tp>::__sqrt3()
+                 * __numeric_constants<_Tp>::__pi());
+          __Bip = __x * (__K_nu / __numeric_constants<_Tp>::__pi()
+                      + _Tp(2) * __I_nu
+                      / __numeric_constants<_Tp>::__sqrt3());
+        }
+      else if (__x < _Tp(0))
+        {
+          _Tp __J_nu, __Jp_nu, __N_nu, __Np_nu;
+
+          __bessel_jn(_Tp(1) / _Tp(3), __z, __J_nu, __N_nu, __Jp_nu, __Np_nu);
+          __Ai = __rootx * (__J_nu
+                    - __N_nu / __numeric_constants<_Tp>::__sqrt3()) / _Tp(2);
+          __Bi = -__rootx * (__N_nu
+                    + __J_nu / __numeric_constants<_Tp>::__sqrt3()) / _Tp(2);
+
+          __bessel_jn(_Tp(2) / _Tp(3), __z, __J_nu, __N_nu, __Jp_nu, __Np_nu);
+          __Aip = __absx * (__N_nu / __numeric_constants<_Tp>::__sqrt3()
+                          + __J_nu) / _Tp(2);
+          __Bip = __absx * (__J_nu / __numeric_constants<_Tp>::__sqrt3()
+                          - __N_nu) / _Tp(2);
+        }
+      else
+        {
+
+
+
+          __Ai = _Tp(0.35502805388781723926L);
+          __Bi = __Ai * __numeric_constants<_Tp>::__sqrt3();
+
+
+
+
+          __Aip = -_Tp(0.25881940379280679840L);
+          __Bip = -__Aip * __numeric_constants<_Tp>::__sqrt3();
+        }
+
+      return;
+    }
+  }
+
+
+
+
+
+}
+# 55 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/poly_hermite.tcc" 1 3
+# 42 "/usr/include/c++/13/tr1/poly_hermite.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 56 "/usr/include/c++/13/tr1/poly_hermite.tcc" 3
+  namespace __detail
+  {
+# 72 "/usr/include/c++/13/tr1/poly_hermite.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __poly_hermite_recursion(unsigned int __n, _Tp __x)
+    {
+
+      _Tp __H_0 = 1;
+      if (__n == 0)
+        return __H_0;
+
+
+      _Tp __H_1 = 2 * __x;
+      if (__n == 1)
+        return __H_1;
+
+
+      _Tp __H_n, __H_nm1, __H_nm2;
+      unsigned int __i;
+      for (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
+        {
+          __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
+          __H_nm2 = __H_nm1;
+          __H_nm1 = __H_n;
+        }
+
+      return __H_n;
+    }
+# 114 "/usr/include/c++/13/tr1/poly_hermite.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __poly_hermite(unsigned int __n, _Tp __x)
+    {
+      if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else
+        return __poly_hermite_recursion(__n, __x);
+    }
+  }
+
+
+
+
+
+}
+# 56 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 1 3
+# 44 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 60 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+  namespace __detail
+  {
+# 75 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_large_n(unsigned __n, _Tpa __alpha1, _Tp __x)
+    {
+      const _Tp __a = -_Tp(__n);
+      const _Tp __b = _Tp(__alpha1) + _Tp(1);
+      const _Tp __eta = _Tp(2) * __b - _Tp(4) * __a;
+      const _Tp __cos2th = __x / __eta;
+      const _Tp __sin2th = _Tp(1) - __cos2th;
+      const _Tp __th = std::acos(std::sqrt(__cos2th));
+      const _Tp __pre_h = __numeric_constants<_Tp>::__pi_2()
+                        * __numeric_constants<_Tp>::__pi_2()
+                        * __eta * __eta * __cos2th * __sin2th;
+
+
+      const _Tp __lg_b = ::std::lgamma(_Tp(__n) + __b);
+      const _Tp __lnfact = ::std::lgamma(_Tp(__n + 1));
+
+
+
+
+
+      _Tp __pre_term1 = _Tp(0.5L) * (_Tp(1) - __b)
+                      * std::log(_Tp(0.25L) * __x * __eta);
+      _Tp __pre_term2 = _Tp(0.25L) * std::log(__pre_h);
+      _Tp __lnpre = __lg_b - __lnfact + _Tp(0.5L) * __x
+                      + __pre_term1 - __pre_term2;
+      _Tp __ser_term1 = std::sin(__a * __numeric_constants<_Tp>::__pi());
+      _Tp __ser_term2 = std::sin(_Tp(0.25L) * __eta
+                              * (_Tp(2) * __th
+                               - std::sin(_Tp(2) * __th))
+                               + __numeric_constants<_Tp>::__pi_4());
+      _Tp __ser = __ser_term1 + __ser_term2;
+
+      return std::exp(__lnpre) * __ser;
+    }
+# 129 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_hyperg(unsigned int __n, _Tpa __alpha1, _Tp __x)
+    {
+      const _Tp __b = _Tp(__alpha1) + _Tp(1);
+      const _Tp __mx = -__x;
+      const _Tp __tc_sgn = (__x < _Tp(0) ? _Tp(1)
+                         : ((__n % 2 == 1) ? -_Tp(1) : _Tp(1)));
+
+      _Tp __tc = _Tp(1);
+      const _Tp __ax = std::abs(__x);
+      for (unsigned int __k = 1; __k <= __n; ++__k)
+        __tc *= (__ax / __k);
+
+      _Tp __term = __tc * __tc_sgn;
+      _Tp __sum = __term;
+      for (int __k = int(__n) - 1; __k >= 0; --__k)
+        {
+          __term *= ((__b + _Tp(__k)) / _Tp(int(__n) - __k))
+                  * _Tp(__k + 1) / __mx;
+          __sum += __term;
+        }
+
+      return __sum;
+    }
+# 185 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre_recursion(unsigned int __n, _Tpa __alpha1, _Tp __x)
+    {
+
+      _Tp __l_0 = _Tp(1);
+      if (__n == 0)
+        return __l_0;
+
+
+      _Tp __l_1 = -__x + _Tp(1) + _Tp(__alpha1);
+      if (__n == 1)
+        return __l_1;
+
+
+      _Tp __l_n2 = __l_0;
+      _Tp __l_n1 = __l_1;
+      _Tp __l_n = _Tp(0);
+      for (unsigned int __nn = 2; __nn <= __n; ++__nn)
+        {
+            __l_n = (_Tp(2 * __nn - 1) + _Tp(__alpha1) - __x)
+                  * __l_n1 / _Tp(__nn)
+                  - (_Tp(__nn - 1) + _Tp(__alpha1)) * __l_n2 / _Tp(__nn);
+            __l_n2 = __l_n1;
+            __l_n1 = __l_n;
+        }
+
+      return __l_n;
+    }
+# 244 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tpa, typename _Tp>
+    _Tp
+    __poly_laguerre(unsigned int __n, _Tpa __alpha1, _Tp __x)
+    {
+      if (__x < _Tp(0))
+        std::__throw_domain_error(("Negative argument " "in __poly_laguerre.")
+                                                            );
+
+      else if (__isnan(__x))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__n == 0)
+        return _Tp(1);
+      else if (__n == 1)
+        return _Tp(1) + _Tp(__alpha1) - __x;
+      else if (__x == _Tp(0))
+        {
+          _Tp __prod = _Tp(__alpha1) + _Tp(1);
+          for (unsigned int __k = 2; __k <= __n; ++__k)
+            __prod *= (_Tp(__alpha1) + _Tp(__k)) / _Tp(__k);
+          return __prod;
+        }
+      else if (__n > 10000000 && _Tp(__alpha1) > -_Tp(1)
+            && __x < _Tp(2) * (_Tp(__alpha1) + _Tp(1)) + _Tp(4 * __n))
+        return __poly_laguerre_large_n(__n, __alpha1, __x);
+      else if (_Tp(__alpha1) >= _Tp(0)
+           || (__x > _Tp(0) && _Tp(__alpha1) < -_Tp(__n + 1)))
+        return __poly_laguerre_recursion(__n, __alpha1, __x);
+      else
+        return __poly_laguerre_hyperg(__n, __alpha1, __x);
+    }
+# 296 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
+    { return __poly_laguerre<unsigned int, _Tp>(__n, __m, __x); }
+# 316 "/usr/include/c++/13/tr1/poly_laguerre.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __laguerre(unsigned int __n, _Tp __x)
+    { return __poly_laguerre<unsigned int, _Tp>(__n, 0, __x); }
+  }
+
+
+
+
+
+
+}
+# 57 "/usr/include/c++/13/bits/specfun.h" 2 3
+# 1 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 1 3
+# 47 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 63 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+  namespace __detail
+  {
+# 78 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_sum(_Tp __s)
+    {
+
+      if (__s < _Tp(1))
+        std::__throw_domain_error(("Bad argument in zeta sum."));
+
+      const unsigned int max_iter = 10000;
+      _Tp __zeta = _Tp(0);
+      for (unsigned int __k = 1; __k < max_iter; ++__k)
+        {
+          _Tp __term = std::pow(static_cast<_Tp>(__k), -__s);
+          if (__term < std::numeric_limits<_Tp>::epsilon())
+            {
+              break;
+            }
+          __zeta += __term;
+        }
+
+      return __zeta;
+    }
+# 115 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_alt(_Tp __s)
+    {
+      _Tp __sgn = _Tp(1);
+      _Tp __zeta = _Tp(0);
+      for (unsigned int __i = 1; __i < 10000000; ++__i)
+        {
+          _Tp __term = __sgn / std::pow(__i, __s);
+          if (std::abs(__term) < std::numeric_limits<_Tp>::epsilon())
+            break;
+          __zeta += __term;
+          __sgn *= _Tp(-1);
+        }
+      __zeta /= _Tp(1) - std::pow(_Tp(2), _Tp(1) - __s);
+
+      return __zeta;
+    }
+# 157 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_glob(_Tp __s)
+    {
+      _Tp __zeta = _Tp(0);
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+      const _Tp __max_bincoeff = std::numeric_limits<_Tp>::max_exponent10
+                               * std::log(_Tp(10)) - _Tp(1);
+
+
+
+      if (__s < _Tp(0))
+        {
+
+          if (::std::fmod(__s,_Tp(2)) == _Tp(0))
+            return _Tp(0);
+          else
+
+            {
+              _Tp __zeta = __riemann_zeta_glob(_Tp(1) - __s);
+              __zeta *= std::pow(_Tp(2)
+                     * __numeric_constants<_Tp>::__pi(), __s)
+                     * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+
+                     * std::exp(::std::lgamma(_Tp(1) - __s))
+
+
+
+                     / __numeric_constants<_Tp>::__pi();
+              return __zeta;
+            }
+        }
+
+      _Tp __num = _Tp(0.5L);
+      const unsigned int __maxit = 10000;
+      for (unsigned int __i = 0; __i < __maxit; ++__i)
+        {
+          bool __punt = false;
+          _Tp __sgn = _Tp(1);
+          _Tp __term = _Tp(0);
+          for (unsigned int __j = 0; __j <= __i; ++__j)
+            {
+
+              _Tp __bincoeff = ::std::lgamma(_Tp(1 + __i))
+                              - ::std::lgamma(_Tp(1 + __j))
+                              - ::std::lgamma(_Tp(1 + __i - __j));
+
+
+
+
+
+              if (__bincoeff > __max_bincoeff)
+                {
+
+                  __punt = true;
+                  break;
+                }
+              __bincoeff = std::exp(__bincoeff);
+              __term += __sgn * __bincoeff * std::pow(_Tp(1 + __j), -__s);
+              __sgn *= _Tp(-1);
+            }
+          if (__punt)
+            break;
+          __term *= __num;
+          __zeta += __term;
+          if (std::abs(__term/__zeta) < __eps)
+            break;
+          __num *= _Tp(0.5L);
+        }
+
+      __zeta /= _Tp(1) - std::pow(_Tp(2), _Tp(1) - __s);
+
+      return __zeta;
+    }
+# 252 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta_product(_Tp __s)
+    {
+      static const _Tp __prime[] = {
+        _Tp(2), _Tp(3), _Tp(5), _Tp(7), _Tp(11), _Tp(13), _Tp(17), _Tp(19),
+        _Tp(23), _Tp(29), _Tp(31), _Tp(37), _Tp(41), _Tp(43), _Tp(47),
+        _Tp(53), _Tp(59), _Tp(61), _Tp(67), _Tp(71), _Tp(73), _Tp(79),
+        _Tp(83), _Tp(89), _Tp(97), _Tp(101), _Tp(103), _Tp(107), _Tp(109)
+      };
+      static const unsigned int __num_primes = sizeof(__prime) / sizeof(_Tp);
+
+      _Tp __zeta = _Tp(1);
+      for (unsigned int __i = 0; __i < __num_primes; ++__i)
+        {
+          const _Tp __fact = _Tp(1) - std::pow(__prime[__i], -__s);
+          __zeta *= __fact;
+          if (_Tp(1) - __fact < std::numeric_limits<_Tp>::epsilon())
+            break;
+        }
+
+      __zeta = _Tp(1) / __zeta;
+
+      return __zeta;
+    }
+# 293 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __riemann_zeta(_Tp __s)
+    {
+      if (__isnan(__s))
+        return std::numeric_limits<_Tp>::quiet_NaN();
+      else if (__s == _Tp(1))
+        return std::numeric_limits<_Tp>::infinity();
+      else if (__s < -_Tp(19))
+        {
+          _Tp __zeta = __riemann_zeta_product(_Tp(1) - __s);
+          __zeta *= std::pow(_Tp(2) * __numeric_constants<_Tp>::__pi(), __s)
+                 * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+
+                 * std::exp(::std::lgamma(_Tp(1) - __s))
+
+
+
+                 / __numeric_constants<_Tp>::__pi();
+          return __zeta;
+        }
+      else if (__s < _Tp(20))
+        {
+
+          bool __glob = true;
+          if (__glob)
+            return __riemann_zeta_glob(__s);
+          else
+            {
+              if (__s > _Tp(1))
+                return __riemann_zeta_sum(__s);
+              else
+                {
+                  _Tp __zeta = std::pow(_Tp(2)
+                                * __numeric_constants<_Tp>::__pi(), __s)
+                         * std::sin(__numeric_constants<_Tp>::__pi_2() * __s)
+
+                             * ::std::tgamma(_Tp(1) - __s)
+
+
+
+                             * __riemann_zeta_sum(_Tp(1) - __s);
+                  return __zeta;
+                }
+            }
+        }
+      else
+        return __riemann_zeta_product(__s);
+    }
+# 365 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    _Tp
+    __hurwitz_zeta_glob(_Tp __a, _Tp __s)
+    {
+      _Tp __zeta = _Tp(0);
+
+      const _Tp __eps = std::numeric_limits<_Tp>::epsilon();
+
+      const _Tp __max_bincoeff = std::numeric_limits<_Tp>::max_exponent10
+                               * std::log(_Tp(10)) - _Tp(1);
+
+      const unsigned int __maxit = 10000;
+      for (unsigned int __i = 0; __i < __maxit; ++__i)
+        {
+          bool __punt = false;
+          _Tp __sgn = _Tp(1);
+          _Tp __term = _Tp(0);
+          for (unsigned int __j = 0; __j <= __i; ++__j)
+            {
+
+              _Tp __bincoeff = ::std::lgamma(_Tp(1 + __i))
+                              - ::std::lgamma(_Tp(1 + __j))
+                              - ::std::lgamma(_Tp(1 + __i - __j));
+
+
+
+
+
+              if (__bincoeff > __max_bincoeff)
+                {
+
+                  __punt = true;
+                  break;
+                }
+              __bincoeff = std::exp(__bincoeff);
+              __term += __sgn * __bincoeff * std::pow(_Tp(__a + __j), -__s);
+              __sgn *= _Tp(-1);
+            }
+          if (__punt)
+            break;
+          __term /= _Tp(__i + 1);
+          if (std::abs(__term / __zeta) < __eps)
+            break;
+          __zeta += __term;
+        }
+
+      __zeta /= __s - _Tp(1);
+
+      return __zeta;
+    }
+# 430 "/usr/include/c++/13/tr1/riemann_zeta.tcc" 3
+    template<typename _Tp>
+    inline _Tp
+    __hurwitz_zeta(_Tp __a, _Tp __s)
+    { return __hurwitz_zeta_glob(__a, __s); }
+  }
+
+
+
+
+
+
+}
+# 58 "/usr/include/c++/13/bits/specfun.h" 2 3
+
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+# 203 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
+  { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
+
+
+
+
+
+
+
+  inline long double
+  assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
+  { return __detail::__assoc_laguerre<long double>(__n, __m, __x); }
+# 248 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__assoc_laguerre<__type>(__n, __m, __x);
+    }
+# 264 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  assoc_legendref(unsigned int __l, unsigned int __m, float __x)
+  { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
+
+
+
+
+
+
+  inline long double
+  assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
+  { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
+# 294 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
+    }
+# 309 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  betaf(float __a, float __b)
+  { return __detail::__beta<float>(__a, __b); }
+
+
+
+
+
+
+
+  inline long double
+  betal(long double __a, long double __b)
+  { return __detail::__beta<long double>(__a, __b); }
+# 339 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpa, typename _Tpb>
+    inline typename __gnu_cxx::__promote_2<_Tpa, _Tpb>::__type
+    beta(_Tpa __a, _Tpb __b)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tpa, _Tpb>::__type __type;
+      return __detail::__beta<__type>(__a, __b);
+    }
+# 355 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  comp_ellint_1f(float __k)
+  { return __detail::__comp_ellint_1<float>(__k); }
+
+
+
+
+
+
+
+  inline long double
+  comp_ellint_1l(long double __k)
+  { return __detail::__comp_ellint_1<long double>(__k); }
+# 387 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    comp_ellint_1(_Tp __k)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__comp_ellint_1<__type>(__k);
+    }
+# 403 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  comp_ellint_2f(float __k)
+  { return __detail::__comp_ellint_2<float>(__k); }
+
+
+
+
+
+
+
+  inline long double
+  comp_ellint_2l(long double __k)
+  { return __detail::__comp_ellint_2<long double>(__k); }
+# 434 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    comp_ellint_2(_Tp __k)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__comp_ellint_2<__type>(__k);
+    }
+# 450 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  comp_ellint_3f(float __k, float __nu)
+  { return __detail::__comp_ellint_3<float>(__k, __nu); }
+
+
+
+
+
+
+
+  inline long double
+  comp_ellint_3l(long double __k, long double __nu)
+  { return __detail::__comp_ellint_3<long double>(__k, __nu); }
+# 485 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp, typename _Tpn>
+    inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
+    comp_ellint_3(_Tp __k, _Tpn __nu)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
+      return __detail::__comp_ellint_3<__type>(__k, __nu);
+    }
+# 501 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  cyl_bessel_if(float __nu, float __x)
+  { return __detail::__cyl_bessel_i<float>(__nu, __x); }
+
+
+
+
+
+
+
+  inline long double
+  cyl_bessel_il(long double __nu, long double __x)
+  { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
+# 531 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpnu, typename _Tp>
+    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
+    cyl_bessel_i(_Tpnu __nu, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
+      return __detail::__cyl_bessel_i<__type>(__nu, __x);
+    }
+# 547 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  cyl_bessel_jf(float __nu, float __x)
+  { return __detail::__cyl_bessel_j<float>(__nu, __x); }
+
+
+
+
+
+
+
+  inline long double
+  cyl_bessel_jl(long double __nu, long double __x)
+  { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
+# 577 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpnu, typename _Tp>
+    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
+    cyl_bessel_j(_Tpnu __nu, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
+      return __detail::__cyl_bessel_j<__type>(__nu, __x);
+    }
+# 593 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  cyl_bessel_kf(float __nu, float __x)
+  { return __detail::__cyl_bessel_k<float>(__nu, __x); }
+
+
+
+
+
+
+
+  inline long double
+  cyl_bessel_kl(long double __nu, long double __x)
+  { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
+# 629 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpnu, typename _Tp>
+    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
+    cyl_bessel_k(_Tpnu __nu, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
+      return __detail::__cyl_bessel_k<__type>(__nu, __x);
+    }
+# 645 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  cyl_neumannf(float __nu, float __x)
+  { return __detail::__cyl_neumann_n<float>(__nu, __x); }
+
+
+
+
+
+
+
+  inline long double
+  cyl_neumannl(long double __nu, long double __x)
+  { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
+# 677 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpnu, typename _Tp>
+    inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
+    cyl_neumann(_Tpnu __nu, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
+      return __detail::__cyl_neumann_n<__type>(__nu, __x);
+    }
+# 693 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  ellint_1f(float __k, float __phi)
+  { return __detail::__ellint_1<float>(__k, __phi); }
+
+
+
+
+
+
+
+  inline long double
+  ellint_1l(long double __k, long double __phi)
+  { return __detail::__ellint_1<long double>(__k, __phi); }
+# 725 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp, typename _Tpp>
+    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
+    ellint_1(_Tp __k, _Tpp __phi)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
+      return __detail::__ellint_1<__type>(__k, __phi);
+    }
+# 741 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  ellint_2f(float __k, float __phi)
+  { return __detail::__ellint_2<float>(__k, __phi); }
+
+
+
+
+
+
+
+  inline long double
+  ellint_2l(long double __k, long double __phi)
+  { return __detail::__ellint_2<long double>(__k, __phi); }
+# 773 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp, typename _Tpp>
+    inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
+    ellint_2(_Tp __k, _Tpp __phi)
+    {
+      typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
+      return __detail::__ellint_2<__type>(__k, __phi);
+    }
+# 789 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  ellint_3f(float __k, float __nu, float __phi)
+  { return __detail::__ellint_3<float>(__k, __nu, __phi); }
+
+
+
+
+
+
+
+  inline long double
+  ellint_3l(long double __k, long double __nu, long double __phi)
+  { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
+# 826 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp, typename _Tpn, typename _Tpp>
+    inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
+    ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
+    {
+      typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
+      return __detail::__ellint_3<__type>(__k, __nu, __phi);
+    }
+# 841 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  expintf(float __x)
+  { return __detail::__expint<float>(__x); }
+
+
+
+
+
+
+
+  inline long double
+  expintl(long double __x)
+  { return __detail::__expint<long double>(__x); }
+# 866 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    expint(_Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__expint<__type>(__x);
+    }
+# 882 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  hermitef(unsigned int __n, float __x)
+  { return __detail::__poly_hermite<float>(__n, __x); }
+
+
+
+
+
+
+
+  inline long double
+  hermitel(unsigned int __n, long double __x)
+  { return __detail::__poly_hermite<long double>(__n, __x); }
+# 914 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    hermite(unsigned int __n, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__poly_hermite<__type>(__n, __x);
+    }
+# 930 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  laguerref(unsigned int __n, float __x)
+  { return __detail::__laguerre<float>(__n, __x); }
+
+
+
+
+
+
+
+  inline long double
+  laguerrel(unsigned int __n, long double __x)
+  { return __detail::__laguerre<long double>(__n, __x); }
+# 958 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    laguerre(unsigned int __n, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__laguerre<__type>(__n, __x);
+    }
+# 974 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  legendref(unsigned int __l, float __x)
+  { return __detail::__poly_legendre_p<float>(__l, __x); }
+
+
+
+
+
+
+
+  inline long double
+  legendrel(unsigned int __l, long double __x)
+  { return __detail::__poly_legendre_p<long double>(__l, __x); }
+# 1003 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    legendre(unsigned int __l, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__poly_legendre_p<__type>(__l, __x);
+    }
+# 1019 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  riemann_zetaf(float __s)
+  { return __detail::__riemann_zeta<float>(__s); }
+
+
+
+
+
+
+
+  inline long double
+  riemann_zetal(long double __s)
+  { return __detail::__riemann_zeta<long double>(__s); }
+# 1054 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    riemann_zeta(_Tp __s)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__riemann_zeta<__type>(__s);
+    }
+# 1070 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  sph_besself(unsigned int __n, float __x)
+  { return __detail::__sph_bessel<float>(__n, __x); }
+
+
+
+
+
+
+
+  inline long double
+  sph_bessell(unsigned int __n, long double __x)
+  { return __detail::__sph_bessel<long double>(__n, __x); }
+# 1098 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    sph_bessel(unsigned int __n, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__sph_bessel<__type>(__n, __x);
+    }
+# 1114 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  sph_legendref(unsigned int __l, unsigned int __m, float __theta)
+  { return __detail::__sph_legendre<float>(__l, __m, __theta); }
+# 1125 "/usr/include/c++/13/bits/specfun.h" 3
+  inline long double
+  sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
+  { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
+# 1145 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__sph_legendre<__type>(__l, __m, __theta);
+    }
+# 1161 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  sph_neumannf(unsigned int __n, float __x)
+  { return __detail::__sph_neumann<float>(__n, __x); }
+
+
+
+
+
+
+
+  inline long double
+  sph_neumannl(unsigned int __n, long double __x)
+  { return __detail::__sph_neumann<long double>(__n, __x); }
+# 1189 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    sph_neumann(unsigned int __n, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      return __detail::__sph_neumann<__type>(__n, __x);
+    }
+
+
+
+
+}
+
+
+namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
+{
+
+# 1216 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  airy_aif(float __x)
+  {
+    float __Ai, __Bi, __Aip, __Bip;
+    std::__detail::__airy<float>(__x, __Ai, __Bi, __Aip, __Bip);
+    return __Ai;
+  }
+
+
+
+
+  inline long double
+  airy_ail(long double __x)
+  {
+    long double __Ai, __Bi, __Aip, __Bip;
+    std::__detail::__airy<long double>(__x, __Ai, __Bi, __Aip, __Bip);
+    return __Ai;
+  }
+
+
+
+
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    airy_ai(_Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      __type __Ai, __Bi, __Aip, __Bip;
+      std::__detail::__airy<__type>(__x, __Ai, __Bi, __Aip, __Bip);
+      return __Ai;
+    }
+
+
+
+
+  inline float
+  airy_bif(float __x)
+  {
+    float __Ai, __Bi, __Aip, __Bip;
+    std::__detail::__airy<float>(__x, __Ai, __Bi, __Aip, __Bip);
+    return __Bi;
+  }
+
+
+
+
+  inline long double
+  airy_bil(long double __x)
+  {
+    long double __Ai, __Bi, __Aip, __Bip;
+    std::__detail::__airy<long double>(__x, __Ai, __Bi, __Aip, __Bip);
+    return __Bi;
+  }
+
+
+
+
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    airy_bi(_Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+      __type __Ai, __Bi, __Aip, __Bip;
+      std::__detail::__airy<__type>(__x, __Ai, __Bi, __Aip, __Bip);
+      return __Bi;
+    }
+# 1292 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  conf_hypergf(float __a, float __c, float __x)
+  { return std::__detail::__conf_hyperg<float>(__a, __c, __x); }
+# 1303 "/usr/include/c++/13/bits/specfun.h" 3
+  inline long double
+  conf_hypergl(long double __a, long double __c, long double __x)
+  { return std::__detail::__conf_hyperg<long double>(__a, __c, __x); }
+# 1323 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpa, typename _Tpc, typename _Tp>
+    inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
+    conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
+      return std::__detail::__conf_hyperg<__type>(__a, __c, __x);
+    }
+# 1340 "/usr/include/c++/13/bits/specfun.h" 3
+  inline float
+  hypergf(float __a, float __b, float __c, float __x)
+  { return std::__detail::__hyperg<float>(__a, __b, __c, __x); }
+# 1351 "/usr/include/c++/13/bits/specfun.h" 3
+  inline long double
+  hypergl(long double __a, long double __b, long double __c, long double __x)
+  { return std::__detail::__hyperg<long double>(__a, __b, __c, __x); }
+# 1372 "/usr/include/c++/13/bits/specfun.h" 3
+  template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
+    inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
+    hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
+    {
+      typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>
+  ::__type __type;
+      return std::__detail::__hyperg<__type>(__a, __b, __c, __x);
+    }
+
+
+
+}
+# 3700 "/usr/include/c++/13/cmath" 2 3
+
+
+}
+# 30 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 2
+# 1 "/usr/include/c++/13/cstdarg" 1 3
+# 39 "/usr/include/c++/13/cstdarg" 3
+       
+# 40 "/usr/include/c++/13/cstdarg" 3
+
+
+
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdarg.h" 1 3 4
+# 40 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdarg.h" 3 4
+typedef __builtin_va_list __gnuc_va_list;
+# 103 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdarg.h" 3 4
+typedef __gnuc_va_list va_list;
+# 44 "/usr/include/c++/13/cstdarg" 2 3
+# 53 "/usr/include/c++/13/cstdarg" 3
+namespace std
+{
+  using ::va_list;
+}
+# 31 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 2
+
+# 1 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 1
+# 34 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+# 1 "/usr/include/c++/13/cstdlib" 1 3
+# 39 "/usr/include/c++/13/cstdlib" 3
+       
+# 40 "/usr/include/c++/13/cstdlib" 3
+# 125 "/usr/include/c++/13/cstdlib" 3
+extern "C++"
+{
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  using ::div_t;
+  using ::ldiv_t;
+
+  using ::abort;
+
+  using ::aligned_alloc;
+
+  using ::atexit;
+
+
+  using ::at_quick_exit;
+
+
+  using ::atof;
+  using ::atoi;
+  using ::atol;
+  using ::bsearch;
+  using ::calloc;
+  using ::div;
+  using ::exit;
+  using ::free;
+  using ::getenv;
+  using ::labs;
+  using ::ldiv;
+  using ::malloc;
+
+  using ::mblen;
+  using ::mbstowcs;
+  using ::mbtowc;
+
+  using ::qsort;
+
+
+  using ::quick_exit;
+
+
+  using ::rand;
+  using ::realloc;
+  using ::srand;
+  using ::strtod;
+  using ::strtol;
+  using ::strtoul;
+  using ::system;
+
+  using ::wcstombs;
+  using ::wctomb;
+
+
+
+  inline ldiv_t
+  div(long __i, long __j) noexcept { return ldiv(__i, __j); }
+
+
+
+
+}
+# 199 "/usr/include/c++/13/cstdlib" 3
+namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
+{
+
+
+
+  using ::lldiv_t;
+
+
+
+
+
+  using ::_Exit;
+
+
+
+  using ::llabs;
+
+  inline lldiv_t
+  div(long long __n, long long __d)
+  { lldiv_t __q; __q.quot = __n / __d; __q.rem = __n % __d; return __q; }
+
+  using ::lldiv;
+# 231 "/usr/include/c++/13/cstdlib" 3
+  using ::atoll;
+  using ::strtoll;
+  using ::strtoull;
+
+  using ::strtof;
+  using ::strtold;
+
+
+}
+
+namespace std
+{
+
+  using ::__gnu_cxx::lldiv_t;
+
+  using ::__gnu_cxx::_Exit;
+
+  using ::__gnu_cxx::llabs;
+  using ::__gnu_cxx::div;
+  using ::__gnu_cxx::lldiv;
+
+  using ::__gnu_cxx::atoll;
+  using ::__gnu_cxx::strtof;
+  using ::__gnu_cxx::strtoll;
+  using ::__gnu_cxx::strtoull;
+  using ::__gnu_cxx::strtold;
+}
+
+
+
+}
+# 35 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 2
+# 1 "/usr/include/c++/13/cstring" 1 3
+# 39 "/usr/include/c++/13/cstring" 3
+       
+# 40 "/usr/include/c++/13/cstring" 3
+
+
+# 1 "/usr/include/string.h" 1 3 4
+# 26 "/usr/include/string.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
+# 27 "/usr/include/string.h" 2 3 4
+
+extern "C" {
+
+
+
+
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 1 3 4
+# 34 "/usr/include/string.h" 2 3 4
+# 43 "/usr/include/string.h" 3 4
+extern void *memcpy (void *__restrict __dest, const void *__restrict __src,
+       size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern void *memmove (void *__dest, const void *__src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+
+extern void *memccpy (void *__restrict __dest, const void *__restrict __src,
+        int __c, size_t __n)
+    noexcept (true) __attribute__ ((__nonnull__ (1, 2))) __attribute__ ((__access__ (__write_only__, 1, 4)));
+
+
+
+
+extern void *memset (void *__s, int __c, size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+extern int memcmp (const void *__s1, const void *__s2, size_t __n)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+# 80 "/usr/include/string.h" 3 4
+extern int __memcmpeq (const void *__s1, const void *__s2, size_t __n)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+extern "C++"
+{
+extern void *memchr (void *__s, int __c, size_t __n)
+      noexcept (true) __asm ("memchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern const void *memchr (const void *__s, int __c, size_t __n)
+      noexcept (true) __asm ("memchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 105 "/usr/include/string.h" 3 4
+}
+# 115 "/usr/include/string.h" 3 4
+extern "C++" void *rawmemchr (void *__s, int __c)
+     noexcept (true) __asm ("rawmemchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern "C++" const void *rawmemchr (const void *__s, int __c)
+     noexcept (true) __asm ("rawmemchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+
+
+extern "C++" void *memrchr (void *__s, int __c, size_t __n)
+      noexcept (true) __asm ("memrchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)))
+      __attribute__ ((__access__ (__read_only__, 1, 3)));
+extern "C++" const void *memrchr (const void *__s, int __c, size_t __n)
+      noexcept (true) __asm ("memrchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)))
+      __attribute__ ((__access__ (__read_only__, 1, 3)));
+# 141 "/usr/include/string.h" 3 4
+extern char *strcpy (char *__restrict __dest, const char *__restrict __src)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+extern char *strncpy (char *__restrict __dest,
+        const char *__restrict __src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern char *strcat (char *__restrict __dest, const char *__restrict __src)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+extern char *strncat (char *__restrict __dest, const char *__restrict __src,
+        size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int strcmp (const char *__s1, const char *__s2)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+extern int strncmp (const char *__s1, const char *__s2, size_t __n)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int strcoll (const char *__s1, const char *__s2)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+extern size_t strxfrm (char *__restrict __dest,
+         const char *__restrict __src, size_t __n)
+    noexcept (true) __attribute__ ((__nonnull__ (2))) __attribute__ ((__access__ (__write_only__, 1, 3)));
+
+
+
+
+
+
+extern int strcoll_l (const char *__s1, const char *__s2, locale_t __l)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));
+
+
+extern size_t strxfrm_l (char *__dest, const char *__src, size_t __n,
+    locale_t __l) noexcept (true) __attribute__ ((__nonnull__ (2, 4)))
+     __attribute__ ((__access__ (__write_only__, 1, 3)));
+
+
+
+
+
+extern char *strdup (const char *__s)
+     noexcept (true) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+
+
+extern char *strndup (const char *__string, size_t __n)
+     noexcept (true) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));
+# 224 "/usr/include/string.h" 3 4
+extern "C++"
+{
+extern char *strchr (char *__s, int __c)
+     noexcept (true) __asm ("strchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern const char *strchr (const char *__s, int __c)
+     noexcept (true) __asm ("strchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 244 "/usr/include/string.h" 3 4
+}
+
+
+
+
+
+
+extern "C++"
+{
+extern char *strrchr (char *__s, int __c)
+     noexcept (true) __asm ("strrchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern const char *strrchr (const char *__s, int __c)
+     noexcept (true) __asm ("strrchr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 271 "/usr/include/string.h" 3 4
+}
+# 281 "/usr/include/string.h" 3 4
+extern "C++" char *strchrnul (char *__s, int __c)
+     noexcept (true) __asm ("strchrnul") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern "C++" const char *strchrnul (const char *__s, int __c)
+     noexcept (true) __asm ("strchrnul") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 293 "/usr/include/string.h" 3 4
+extern size_t strcspn (const char *__s, const char *__reject)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern size_t strspn (const char *__s, const char *__accept)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern "C++"
+{
+extern char *strpbrk (char *__s, const char *__accept)
+     noexcept (true) __asm ("strpbrk") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+extern const char *strpbrk (const char *__s, const char *__accept)
+     noexcept (true) __asm ("strpbrk") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+# 321 "/usr/include/string.h" 3 4
+}
+
+
+
+
+
+
+extern "C++"
+{
+extern char *strstr (char *__haystack, const char *__needle)
+     noexcept (true) __asm ("strstr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+extern const char *strstr (const char *__haystack, const char *__needle)
+     noexcept (true) __asm ("strstr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+# 348 "/usr/include/string.h" 3 4
+}
+
+
+
+
+
+
+
+extern char *strtok (char *__restrict __s, const char *__restrict __delim)
+     noexcept (true) __attribute__ ((__nonnull__ (2)));
+
+
+
+extern char *__strtok_r (char *__restrict __s,
+    const char *__restrict __delim,
+    char **__restrict __save_ptr)
+     noexcept (true) __attribute__ ((__nonnull__ (2, 3)));
+
+extern char *strtok_r (char *__restrict __s, const char *__restrict __delim,
+         char **__restrict __save_ptr)
+     noexcept (true) __attribute__ ((__nonnull__ (2, 3)));
+
+
+
+
+
+extern "C++" char *strcasestr (char *__haystack, const char *__needle)
+     noexcept (true) __asm ("strcasestr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+extern "C++" const char *strcasestr (const char *__haystack,
+         const char *__needle)
+     noexcept (true) __asm ("strcasestr") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+# 389 "/usr/include/string.h" 3 4
+extern void *memmem (const void *__haystack, size_t __haystacklen,
+       const void *__needle, size_t __needlelen)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 3)))
+    __attribute__ ((__access__ (__read_only__, 1, 2)))
+    __attribute__ ((__access__ (__read_only__, 3, 4)));
+
+
+
+extern void *__mempcpy (void *__restrict __dest,
+   const void *__restrict __src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern void *mempcpy (void *__restrict __dest,
+        const void *__restrict __src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+extern size_t strlen (const char *__s)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+extern size_t strnlen (const char *__string, size_t __maxlen)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+
+
+
+
+extern char *strerror (int __errnum) noexcept (true);
+# 444 "/usr/include/string.h" 3 4
+extern char *strerror_r (int __errnum, char *__buf, size_t __buflen)
+     noexcept (true) __attribute__ ((__nonnull__ (2))) __attribute__ ((__access__ (__write_only__, 2, 3)));
+
+
+
+
+extern const char *strerrordesc_np (int __err) noexcept (true);
+
+extern const char *strerrorname_np (int __err) noexcept (true);
+
+
+
+
+
+extern char *strerror_l (int __errnum, locale_t __l) noexcept (true);
+
+
+
+# 1 "/usr/include/strings.h" 1 3 4
+# 23 "/usr/include/strings.h" 3 4
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stddef.h" 1 3 4
+# 24 "/usr/include/strings.h" 2 3 4
+
+
+
+
+
+
+extern "C" {
+
+
+
+extern int bcmp (const void *__s1, const void *__s2, size_t __n)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern void bcopy (const void *__src, void *__dest, size_t __n)
+  noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern void bzero (void *__s, size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+
+extern "C++"
+{
+extern char *index (char *__s, int __c)
+     noexcept (true) __asm ("index") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern const char *index (const char *__s, int __c)
+     noexcept (true) __asm ("index") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 66 "/usr/include/strings.h" 3 4
+}
+
+
+
+
+
+
+
+extern "C++"
+{
+extern char *rindex (char *__s, int __c)
+     noexcept (true) __asm ("rindex") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+extern const char *rindex (const char *__s, int __c)
+     noexcept (true) __asm ("rindex") __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
+# 94 "/usr/include/strings.h" 3 4
+}
+# 104 "/usr/include/strings.h" 3 4
+extern int ffs (int __i) noexcept (true) __attribute__ ((__const__));
+
+
+
+
+
+extern int ffsl (long int __l) noexcept (true) __attribute__ ((__const__));
+__extension__ extern int ffsll (long long int __ll)
+     noexcept (true) __attribute__ ((__const__));
+
+
+
+extern int strcasecmp (const char *__s1, const char *__s2)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern int strncasecmp (const char *__s1, const char *__s2, size_t __n)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+
+
+extern int strcasecmp_l (const char *__s1, const char *__s2, locale_t __loc)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));
+
+
+
+extern int strncasecmp_l (const char *__s1, const char *__s2,
+     size_t __n, locale_t __loc)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 4)));
+
+
+}
+# 463 "/usr/include/string.h" 2 3 4
+
+
+
+extern void explicit_bzero (void *__s, size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1)))
+    __attribute__ ((__access__ (__write_only__, 1, 2)));
+
+
+
+extern char *strsep (char **__restrict __stringp,
+       const char *__restrict __delim)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+extern char *strsignal (int __sig) noexcept (true);
+
+
+
+extern const char *sigabbrev_np (int __sig) noexcept (true);
+
+
+extern const char *sigdescr_np (int __sig) noexcept (true);
+
+
+
+extern char *__stpcpy (char *__restrict __dest, const char *__restrict __src)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern char *stpcpy (char *__restrict __dest, const char *__restrict __src)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+extern char *__stpncpy (char *__restrict __dest,
+   const char *__restrict __src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+extern char *stpncpy (char *__restrict __dest,
+        const char *__restrict __src, size_t __n)
+     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
+
+
+
+
+extern size_t strlcpy (char *__restrict __dest,
+         const char *__restrict __src, size_t __n)
+  noexcept (true) __attribute__ ((__nonnull__ (1, 2))) __attribute__ ((__access__ (__write_only__, 1, 3)));
+
+
+
+extern size_t strlcat (char *__restrict __dest,
+         const char *__restrict __src, size_t __n)
+  noexcept (true) __attribute__ ((__nonnull__ (1, 2))) __attribute__ ((__access__ (__read_write__, 1, 3)));
+
+
+
+
+extern int strverscmp (const char *__s1, const char *__s2)
+     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
+
+
+extern char *strfry (char *__string) noexcept (true) __attribute__ ((__nonnull__ (1)));
+
+
+extern void *memfrob (void *__s, size_t __n) noexcept (true) __attribute__ ((__nonnull__ (1)))
+    __attribute__ ((__access__ (__read_write__, 1, 2)));
+
+
+
+
+
+
+
+extern "C++" char *basename (char *__filename)
+     noexcept (true) __asm ("basename") __attribute__ ((__nonnull__ (1)));
+extern "C++" const char *basename (const char *__filename)
+     noexcept (true) __asm ("basename") __attribute__ ((__nonnull__ (1)));
+# 552 "/usr/include/string.h" 3 4
+}
+# 43 "/usr/include/c++/13/cstring" 2 3
+# 71 "/usr/include/c++/13/cstring" 3
+extern "C++"
+{
+namespace std __attribute__ ((__visibility__ ("default")))
+{
+
+
+  using ::memchr;
+  using ::memcmp;
+  using ::memcpy;
+  using ::memmove;
+  using ::memset;
+  using ::strcat;
+  using ::strcmp;
+  using ::strcoll;
+  using ::strcpy;
+  using ::strcspn;
+  using ::strerror;
+  using ::strlen;
+  using ::strncat;
+  using ::strncmp;
+  using ::strncpy;
+  using ::strspn;
+  using ::strtok;
+  using ::strxfrm;
+  using ::strchr;
+  using ::strpbrk;
+  using ::strrchr;
+  using ::strstr;
+# 122 "/usr/include/c++/13/cstring" 3
+
+}
+}
+# 36 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 2
+# 44 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+# 1 "/usr/include/c++/13/cassert" 1 3
+# 41 "/usr/include/c++/13/cassert" 3
+       
+# 42 "/usr/include/c++/13/cassert" 3
+
+
+# 1 "/usr/include/assert.h" 1 3 4
+# 66 "/usr/include/assert.h" 3 4
+extern "C" {
+
+
+extern void __assert_fail (const char *__assertion, const char *__file,
+      unsigned int __line, const char *__function)
+     noexcept (true) __attribute__ ((__noreturn__));
+
+
+extern void __assert_perror_fail (int __errnum, const char *__file,
+      unsigned int __line, const char *__function)
+     noexcept (true) __attribute__ ((__noreturn__));
+
+
+
+
+extern void __assert (const char *__assertion, const char *__file, int __line)
+     noexcept (true) __attribute__ ((__noreturn__));
+
+
+}
+# 45 "/usr/include/c++/13/cassert" 2 3
+# 45 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 2
+# 186 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+# 1 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdint.h" 1 3 4
+# 9 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdint.h" 3 4
+# 1 "/usr/include/stdint.h" 1 3 4
+# 26 "/usr/include/stdint.h" 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/libc-header-start.h" 1 3 4
+# 27 "/usr/include/stdint.h" 2 3 4
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/wchar.h" 1 3 4
+# 29 "/usr/include/stdint.h" 2 3 4
+# 1 "/usr/include/aarch64-linux-gnu/bits/wordsize.h" 1 3 4
+# 30 "/usr/include/stdint.h" 2 3 4
+
+
+
+
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/stdint-uintn.h" 1 3 4
+# 24 "/usr/include/aarch64-linux-gnu/bits/stdint-uintn.h" 3 4
+typedef __uint8_t uint8_t;
+typedef __uint16_t uint16_t;
+typedef __uint32_t uint32_t;
+typedef __uint64_t uint64_t;
+# 38 "/usr/include/stdint.h" 2 3 4
+
+
+
+# 1 "/usr/include/aarch64-linux-gnu/bits/stdint-least.h" 1 3 4
+# 25 "/usr/include/aarch64-linux-gnu/bits/stdint-least.h" 3 4
+typedef __int_least8_t int_least8_t;
+typedef __int_least16_t int_least16_t;
+typedef __int_least32_t int_least32_t;
+typedef __int_least64_t int_least64_t;
+
+
+typedef __uint_least8_t uint_least8_t;
+typedef __uint_least16_t uint_least16_t;
+typedef __uint_least32_t uint_least32_t;
+typedef __uint_least64_t uint_least64_t;
+# 42 "/usr/include/stdint.h" 2 3 4
+
+
+
+
+
+typedef signed char int_fast8_t;
+
+typedef long int int_fast16_t;
+typedef long int int_fast32_t;
+typedef long int int_fast64_t;
+# 60 "/usr/include/stdint.h" 3 4
+typedef unsigned char uint_fast8_t;
+
+typedef unsigned long int uint_fast16_t;
+typedef unsigned long int uint_fast32_t;
+typedef unsigned long int uint_fast64_t;
+# 76 "/usr/include/stdint.h" 3 4
+typedef long int intptr_t;
+
+
+typedef unsigned long int uintptr_t;
+# 90 "/usr/include/stdint.h" 3 4
+typedef __intmax_t intmax_t;
+typedef __uintmax_t uintmax_t;
+# 10 "/usr/lib/gcc/aarch64-linux-gnu/13/include/stdint.h" 2 3 4
+# 187 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 2
+
+
+
+
+# 190 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+typedef uint16_t uc16;
+# 239 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+namespace double_conversion {
+
+inline int StrLength(const char* string) {
+  size_t length = strlen(string);
+  
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+ (static_cast <bool> (
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+ length == static_cast<size_t>(static_cast<int>(length))
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+ ) ? void (0) : __assert_fail (
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+ "length == static_cast<size_t>(static_cast<int>(length))"
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 243 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                                  ;
+  return static_cast<int>(length);
+}
+
+
+template <typename T>
+class Vector {
+ public:
+  Vector() : start_(nullptr), length_(0) {}
+  Vector(T* data, int len) : start_(data), length_(len) {
+    
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   len == 0 || (len > 0 && data != nullptr)
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "len == 0 || (len > 0 && data != nullptr)"
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 253 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                                       ;
+  }
+
+
+
+  Vector<T> SubVector(int from, int to) {
+    
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   to <= length_
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "to <= length_"
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 259 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                          ;
+    
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   from < to
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "from < to"
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 260 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                      ;
+    
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   0 <= from
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "0 <= from"
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 261 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                      ;
+    return Vector<T>(start() + from, to - from);
+  }
+
+
+  int length() const { return length_; }
+
+
+  bool is_empty() const { return length_ == 0; }
+
+
+  T* start() const { return start_; }
+
+
+  T& operator[](int index) const {
+    
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   0 <= index && index < length_
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "0 <= index && index < length_"
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 276 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                          ;
+    return start_[index];
+  }
+
+  T& first() { return start_[0]; }
+
+  T& last() { return start_[length_ - 1]; }
+
+  void pop_back() {
+    
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   !is_empty()
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "!is_empty()"
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 285 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                        ;
+    --length_;
+  }
+
+ private:
+  T* start_;
+  int length_;
+};
+
+
+
+
+
+class StringBuilder {
+ public:
+  StringBuilder(char* buffer, int buffer_size)
+      : buffer_(buffer, buffer_size), position_(0) { }
+
+  ~StringBuilder() { if (!is_finalized()) Finalize(); }
+
+  int size() const { return buffer_.length(); }
+
+
+  int position() const {
+    
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   !is_finalized()
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "!is_finalized()"
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 309 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                            ;
+    return position_;
+  }
+
+
+  void Reset() { position_ = 0; }
+
+
+
+
+  void AddCharacter(char c) {
+    
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   c != '\0'
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "c != '\\0'"
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 320 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                      ;
+    
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   !is_finalized() && position_ < buffer_.length()
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "!is_finalized() && position_ < buffer_.length()"
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 321 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                            ;
+    buffer_[position_++] = c;
+  }
+
+
+
+  void AddString(const char* s) {
+    AddSubstring(s, StrLength(s));
+  }
+
+
+
+  void AddSubstring(const char* s, int n) {
+    
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   !is_finalized() && position_ + n < buffer_.length()
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "!is_finalized() && position_ + n < buffer_.length()"
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 334 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                                ;
+    
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   static_cast<size_t>(n) <= strlen(s)
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "static_cast<size_t>(n) <= strlen(s)"
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 335 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                ;
+    memmove(&buffer_[position_], s, static_cast<size_t>(n));
+    position_ += n;
+  }
+
+
+
+
+  void AddPadding(char c, int count) {
+    for (int i = 0; i < count; i++) {
+      AddCharacter(c);
+    }
+  }
+
+
+  char* Finalize() {
+    
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   !is_finalized() && position_ < buffer_.length()
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "!is_finalized() && position_ < buffer_.length()"
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 351 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                            ;
+    buffer_[position_] = '\0';
+
+
+    
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   strlen(buffer_.start()) == static_cast<size_t>(position_)
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "strlen(buffer_.start()) == static_cast<size_t>(position_)"
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 355 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                                                                      ;
+    position_ = -1;
+    
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   (static_cast <bool> (
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   is_finalized()
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+   "is_finalized()"
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 357 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+                                           ;
+    return buffer_.start();
+  }
+
+ private:
+  Vector<char> buffer_;
+  int position_;
+
+  bool is_finalized() const { return position_ < 0; }
+
+  StringBuilder(); StringBuilder(const StringBuilder&); void operator=(const StringBuilder&);
+};
+# 394 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/utils.h"
+template <class Dest, class Source>
+Dest BitCast(const Source& source) {
+
+
+
+  static_assert(sizeof(Dest) == sizeof(Source),
+                "source and destination size mismatch");
+
+
+
+
+
+  Dest dest;
+  memmove(&dest, &source, sizeof(dest));
+  return dest;
+}
+
+template <class Dest, class Source>
+Dest BitCast(Source* source) {
+  return BitCast<Dest>(reinterpret_cast<uintptr_t>(source));
+}
+
+}
+# 33 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 2
+
+# 1 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.h" 1
+# 31 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.h"
+# 1 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 1
+# 33 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+namespace double_conversion {
+
+
+
+
+
+
+
+class DiyFp {
+ public:
+  static const int kSignificandSize = 64;
+
+  DiyFp() : f_(0), e_(0) {}
+  DiyFp(const uint64_t significand, const int32_t exponent) : f_(significand), e_(exponent) {}
+
+
+
+
+
+  void Subtract(const DiyFp& other) {
+    
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   (static_cast <bool> (
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   e_ == other.e_
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   "e_ == other.e_"
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 53 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+                                           ;
+    
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   (static_cast <bool> (
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   f_ >= other.f_
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   "f_ >= other.f_"
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 54 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+                                           ;
+    f_ -= other.f_;
+  }
+
+
+
+
+  static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Subtract(b);
+    return result;
+  }
+
+
+  void Multiply(const DiyFp& other) {
+
+
+
+
+    const uint64_t kM32 = 0xFFFFFFFFU;
+    const uint64_t a = f_ >> 32;
+    const uint64_t b = f_ & kM32;
+    const uint64_t c = other.f_ >> 32;
+    const uint64_t d = other.f_ & kM32;
+    const uint64_t ac = a * c;
+    const uint64_t bc = b * c;
+    const uint64_t ad = a * d;
+    const uint64_t bd = b * d;
+
+
+    const uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32) + (1U << 31);
+    e_ += other.e_ + 64;
+    f_ = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
+  }
+
+
+  static DiyFp Times(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Multiply(b);
+    return result;
+  }
+
+  void Normalize() {
+    
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   (static_cast <bool> (
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   f_ != 0
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   ) ? void (0) : __assert_fail (
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+   "f_ != 0"
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h" 3 4
+   , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 97 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/diy-fp.h"
+                                    ;
+    uint64_t significand = f_;
+    int32_t exponent = e_;
+
+
+
+    const uint64_t k10MSBits = (((static_cast<uint64_t>(0xFFC00000) << 32) + 0x00000000u));
+    while ((significand & k10MSBits) == 0) {
+      significand <<= 10;
+      exponent -= 10;
+    }
+    while ((significand & kUint64MSB) == 0) {
+      significand <<= 1;
+      exponent--;
+    }
+    f_ = significand;
+    e_ = exponent;
+  }
+
+  static DiyFp Normalize(const DiyFp& a) {
+    DiyFp result = a;
+    result.Normalize();
+    return result;
+  }
+
+  uint64_t f() const { return f_; }
+  int32_t e() const { return e_; }
+
+  void set_f(uint64_t new_value) { f_ = new_value; }
+  void set_e(int32_t new_value) { e_ = new_value; }
+
+ private:
+  static const uint64_t kUint64MSB = (((static_cast<uint64_t>(0x80000000) << 32) + 0x00000000u));
+
+  uint64_t f_;
+  int32_t e_;
+};
+
+}
+# 32 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.h" 2
+
+namespace double_conversion {
+
+namespace PowersOfTenCache {
+
+
+
+  static const int kDecimalExponentDistance = 8;
+
+  static const int kMinDecimalExponent = -348;
+  static const int kMaxDecimalExponent = 340;
+
+
+
+  void GetCachedPowerForBinaryExponentRange(int min_exponent,
+                                            int max_exponent,
+                                            DiyFp* power,
+                                            int* decimal_exponent);
+
+
+
+
+
+
+  void GetCachedPowerForDecimalExponent(int requested_exponent,
+                                        DiyFp* power,
+                                        int* found_exponent);
+
+}
+
+}
+# 35 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 2
+
+namespace double_conversion {
+
+namespace PowersOfTenCache {
+
+struct CachedPower {
+  uint64_t significand;
+  int16_t binary_exponent;
+  int16_t decimal_exponent;
+};
+
+static const CachedPower kCachedPowers[] = {
+  {(((static_cast<uint64_t>(0xfa8fd5a0) << 32) + 0x081c0288u)), -1220, -348},
+  {(((static_cast<uint64_t>(0xbaaee17f) << 32) + 0xa23ebf76u)), -1193, -340},
+  {(((static_cast<uint64_t>(0x8b16fb20) << 32) + 0x3055ac76u)), -1166, -332},
+  {(((static_cast<uint64_t>(0xcf42894a) << 32) + 0x5dce35eau)), -1140, -324},
+  {(((static_cast<uint64_t>(0x9a6bb0aa) << 32) + 0x55653b2du)), -1113, -316},
+  {(((static_cast<uint64_t>(0xe61acf03) << 32) + 0x3d1a45dfu)), -1087, -308},
+  {(((static_cast<uint64_t>(0xab70fe17) << 32) + 0xc79ac6cau)), -1060, -300},
+  {(((static_cast<uint64_t>(0xff77b1fc) << 32) + 0xbebcdc4fu)), -1034, -292},
+  {(((static_cast<uint64_t>(0xbe5691ef) << 32) + 0x416bd60cu)), -1007, -284},
+  {(((static_cast<uint64_t>(0x8dd01fad) << 32) + 0x907ffc3cu)), -980, -276},
+  {(((static_cast<uint64_t>(0xd3515c28) << 32) + 0x31559a83u)), -954, -268},
+  {(((static_cast<uint64_t>(0x9d71ac8f) << 32) + 0xada6c9b5u)), -927, -260},
+  {(((static_cast<uint64_t>(0xea9c2277) << 32) + 0x23ee8bcbu)), -901, -252},
+  {(((static_cast<uint64_t>(0xaecc4991) << 32) + 0x4078536du)), -874, -244},
+  {(((static_cast<uint64_t>(0x823c1279) << 32) + 0x5db6ce57u)), -847, -236},
+  {(((static_cast<uint64_t>(0xc2109436) << 32) + 0x4dfb5637u)), -821, -228},
+  {(((static_cast<uint64_t>(0x9096ea6f) << 32) + 0x3848984fu)), -794, -220},
+  {(((static_cast<uint64_t>(0xd77485cb) << 32) + 0x25823ac7u)), -768, -212},
+  {(((static_cast<uint64_t>(0xa086cfcd) << 32) + 0x97bf97f4u)), -741, -204},
+  {(((static_cast<uint64_t>(0xef340a98) << 32) + 0x172aace5u)), -715, -196},
+  {(((static_cast<uint64_t>(0xb23867fb) << 32) + 0x2a35b28eu)), -688, -188},
+  {(((static_cast<uint64_t>(0x84c8d4df) << 32) + 0xd2c63f3bu)), -661, -180},
+  {(((static_cast<uint64_t>(0xc5dd4427) << 32) + 0x1ad3cdbau)), -635, -172},
+  {(((static_cast<uint64_t>(0x936b9fce) << 32) + 0xbb25c996u)), -608, -164},
+  {(((static_cast<uint64_t>(0xdbac6c24) << 32) + 0x7d62a584u)), -582, -156},
+  {(((static_cast<uint64_t>(0xa3ab6658) << 32) + 0x0d5fdaf6u)), -555, -148},
+  {(((static_cast<uint64_t>(0xf3e2f893) << 32) + 0xdec3f126u)), -529, -140},
+  {(((static_cast<uint64_t>(0xb5b5ada8) << 32) + 0xaaff80b8u)), -502, -132},
+  {(((static_cast<uint64_t>(0x87625f05) << 32) + 0x6c7c4a8bu)), -475, -124},
+  {(((static_cast<uint64_t>(0xc9bcff60) << 32) + 0x34c13053u)), -449, -116},
+  {(((static_cast<uint64_t>(0x964e858c) << 32) + 0x91ba2655u)), -422, -108},
+  {(((static_cast<uint64_t>(0xdff97724) << 32) + 0x70297ebdu)), -396, -100},
+  {(((static_cast<uint64_t>(0xa6dfbd9f) << 32) + 0xb8e5b88fu)), -369, -92},
+  {(((static_cast<uint64_t>(0xf8a95fcf) << 32) + 0x88747d94u)), -343, -84},
+  {(((static_cast<uint64_t>(0xb9447093) << 32) + 0x8fa89bcfu)), -316, -76},
+  {(((static_cast<uint64_t>(0x8a08f0f8) << 32) + 0xbf0f156bu)), -289, -68},
+  {(((static_cast<uint64_t>(0xcdb02555) << 32) + 0x653131b6u)), -263, -60},
+  {(((static_cast<uint64_t>(0x993fe2c6) << 32) + 0xd07b7facu)), -236, -52},
+  {(((static_cast<uint64_t>(0xe45c10c4) << 32) + 0x2a2b3b06u)), -210, -44},
+  {(((static_cast<uint64_t>(0xaa242499) << 32) + 0x697392d3u)), -183, -36},
+  {(((static_cast<uint64_t>(0xfd87b5f2) << 32) + 0x8300ca0eu)), -157, -28},
+  {(((static_cast<uint64_t>(0xbce50864) << 32) + 0x92111aebu)), -130, -20},
+  {(((static_cast<uint64_t>(0x8cbccc09) << 32) + 0x6f5088ccu)), -103, -12},
+  {(((static_cast<uint64_t>(0xd1b71758) << 32) + 0xe219652cu)), -77, -4},
+  {(((static_cast<uint64_t>(0x9c400000) << 32) + 0x00000000u)), -50, 4},
+  {(((static_cast<uint64_t>(0xe8d4a510) << 32) + 0x00000000u)), -24, 12},
+  {(((static_cast<uint64_t>(0xad78ebc5) << 32) + 0xac620000u)), 3, 20},
+  {(((static_cast<uint64_t>(0x813f3978) << 32) + 0xf8940984u)), 30, 28},
+  {(((static_cast<uint64_t>(0xc097ce7b) << 32) + 0xc90715b3u)), 56, 36},
+  {(((static_cast<uint64_t>(0x8f7e32ce) << 32) + 0x7bea5c70u)), 83, 44},
+  {(((static_cast<uint64_t>(0xd5d238a4) << 32) + 0xabe98068u)), 109, 52},
+  {(((static_cast<uint64_t>(0x9f4f2726) << 32) + 0x179a2245u)), 136, 60},
+  {(((static_cast<uint64_t>(0xed63a231) << 32) + 0xd4c4fb27u)), 162, 68},
+  {(((static_cast<uint64_t>(0xb0de6538) << 32) + 0x8cc8ada8u)), 189, 76},
+  {(((static_cast<uint64_t>(0x83c7088e) << 32) + 0x1aab65dbu)), 216, 84},
+  {(((static_cast<uint64_t>(0xc45d1df9) << 32) + 0x42711d9au)), 242, 92},
+  {(((static_cast<uint64_t>(0x924d692c) << 32) + 0xa61be758u)), 269, 100},
+  {(((static_cast<uint64_t>(0xda01ee64) << 32) + 0x1a708deau)), 295, 108},
+  {(((static_cast<uint64_t>(0xa26da399) << 32) + 0x9aef774au)), 322, 116},
+  {(((static_cast<uint64_t>(0xf209787b) << 32) + 0xb47d6b85u)), 348, 124},
+  {(((static_cast<uint64_t>(0xb454e4a1) << 32) + 0x79dd1877u)), 375, 132},
+  {(((static_cast<uint64_t>(0x865b8692) << 32) + 0x5b9bc5c2u)), 402, 140},
+  {(((static_cast<uint64_t>(0xc83553c5) << 32) + 0xc8965d3du)), 428, 148},
+  {(((static_cast<uint64_t>(0x952ab45c) << 32) + 0xfa97a0b3u)), 455, 156},
+  {(((static_cast<uint64_t>(0xde469fbd) << 32) + 0x99a05fe3u)), 481, 164},
+  {(((static_cast<uint64_t>(0xa59bc234) << 32) + 0xdb398c25u)), 508, 172},
+  {(((static_cast<uint64_t>(0xf6c69a72) << 32) + 0xa3989f5cu)), 534, 180},
+  {(((static_cast<uint64_t>(0xb7dcbf53) << 32) + 0x54e9beceu)), 561, 188},
+  {(((static_cast<uint64_t>(0x88fcf317) << 32) + 0xf22241e2u)), 588, 196},
+  {(((static_cast<uint64_t>(0xcc20ce9b) << 32) + 0xd35c78a5u)), 614, 204},
+  {(((static_cast<uint64_t>(0x98165af3) << 32) + 0x7b2153dfu)), 641, 212},
+  {(((static_cast<uint64_t>(0xe2a0b5dc) << 32) + 0x971f303au)), 667, 220},
+  {(((static_cast<uint64_t>(0xa8d9d153) << 32) + 0x5ce3b396u)), 694, 228},
+  {(((static_cast<uint64_t>(0xfb9b7cd9) << 32) + 0xa4a7443cu)), 720, 236},
+  {(((static_cast<uint64_t>(0xbb764c4c) << 32) + 0xa7a44410u)), 747, 244},
+  {(((static_cast<uint64_t>(0x8bab8eef) << 32) + 0xb6409c1au)), 774, 252},
+  {(((static_cast<uint64_t>(0xd01fef10) << 32) + 0xa657842cu)), 800, 260},
+  {(((static_cast<uint64_t>(0x9b10a4e5) << 32) + 0xe9913129u)), 827, 268},
+  {(((static_cast<uint64_t>(0xe7109bfb) << 32) + 0xa19c0c9du)), 853, 276},
+  {(((static_cast<uint64_t>(0xac2820d9) << 32) + 0x623bf429u)), 880, 284},
+  {(((static_cast<uint64_t>(0x80444b5e) << 32) + 0x7aa7cf85u)), 907, 292},
+  {(((static_cast<uint64_t>(0xbf21e440) << 32) + 0x03acdd2du)), 933, 300},
+  {(((static_cast<uint64_t>(0x8e679c2f) << 32) + 0x5e44ff8fu)), 960, 308},
+  {(((static_cast<uint64_t>(0xd433179d) << 32) + 0x9c8cb841u)), 986, 316},
+  {(((static_cast<uint64_t>(0x9e19db92) << 32) + 0xb4e31ba9u)), 1013, 324},
+  {(((static_cast<uint64_t>(0xeb96bf6e) << 32) + 0xbadf77d9u)), 1039, 332},
+  {(((static_cast<uint64_t>(0xaf87023b) << 32) + 0x9bf0ee6bu)), 1066, 340},
+};
+
+static const int kCachedPowersOffset = 348;
+static const double kD_1_LOG2_10 = 0.30102999566398114;
+
+void GetCachedPowerForBinaryExponentRange(
+    int min_exponent,
+    int max_exponent,
+    DiyFp* power,
+    int* decimal_exponent) {
+  int kQ = DiyFp::kSignificandSize;
+  double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
+  int foo = kCachedPowersOffset;
+  int index =
+      (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
+  
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ 0 <= index && index < static_cast<int>(((sizeof(kCachedPowers) / sizeof(*(kCachedPowers))) / static_cast<size_t>(!(sizeof(kCachedPowers) % sizeof(*(kCachedPowers))))))
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "0 <= index && index < static_cast<int>(((sizeof(kCachedPowers) / sizeof(*(kCachedPowers))) / static_cast<size_t>(!(sizeof(kCachedPowers) % sizeof(*(kCachedPowers))))))"
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 149 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                                                              ;
+  CachedPower cached_power = kCachedPowers[index];
+  
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ min_exponent <= cached_power.binary_exponent
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "min_exponent <= cached_power.binary_exponent"
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 151 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                       ;
+  (void) max_exponent;
+  
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ cached_power.binary_exponent <= max_exponent
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "cached_power.binary_exponent <= max_exponent"
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 153 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                       ;
+  *decimal_exponent = cached_power.decimal_exponent;
+  *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
+}
+
+
+void GetCachedPowerForDecimalExponent(int requested_exponent,
+                                      DiyFp* power,
+                                      int* found_exponent) {
+  
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ kMinDecimalExponent <= requested_exponent
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "kMinDecimalExponent <= requested_exponent"
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 162 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                    ;
+  
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance"
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 163 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                                              ;
+  int index =
+      (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
+  CachedPower cached_power = kCachedPowers[index];
+  *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
+  *found_exponent = cached_power.decimal_exponent;
+  
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ *found_exponent <= requested_exponent
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "*found_exponent <= requested_exponent"
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 169 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                ;
+  
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ (static_cast <bool> (
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ requested_exponent < *found_exponent + kDecimalExponentDistance
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ ) ? void (0) : __assert_fail (
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+ "requested_exponent < *found_exponent + kDecimalExponentDistance"
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc" 3 4
+ , __builtin_FILE (), __builtin_LINE (), __extension__ __PRETTY_FUNCTION__))
+# 170 "/tmp/tmpl_i20ey9/double-conversion/double-conversion/cached-powers.cc"
+                                                                                          ;
+}
+
+}
+
+}