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Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,029
22
80,058
Tags: brute force, math, number theory Correct Solution: ``` def check(n): d = 2 while d*d <= n: if n % d == 0: return False d += 1 return True n = int(input()) flag = False if check(n) and n > 10: print(1,'\n',n) elif n >= 9: Ans = [3] n -= 3 for i in range(2,n): if chec...
output
1
40,029
22
80,059
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,030
22
80,060
Tags: brute force, math, number theory Correct Solution: ``` def isPrime(x) : if x == 1: return False if x == 2: return True if x%2 == 0: return False i = 3 while i*i <= x : if x % i == 0 : return False i += 2 return True n = int(input()) if isPrime(n) : ans...
output
1
40,030
22
80,061
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,031
22
80,062
Tags: brute force, math, number theory Correct Solution: ``` import math def is_prime(a): for i in range(2, int(math.sqrt(a) + 1)): if a % i == 0: return False return True def solve(): n, = map(int, input().split()) if is_prime(n): print(1) print(n) retur...
output
1
40,031
22
80,063
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,032
22
80,064
Tags: brute force, math, number theory Correct Solution: ``` def isPrime(n) : if (n==3 or n==2) : return True if (n % 2 == 0 or n % 3 == 0) : return False i = 5 while(i * i <= n) : if (n % i == 0 or n % (i + 2) == 0) : return False i = i + 6 return Tru...
output
1
40,032
22
80,065
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,033
22
80,066
Tags: brute force, math, number theory Correct Solution: ``` l=list() def prime(N): count=0 i=1 while(i*i<=N): if i*i==N: count=count+1 elif N%i==0: count=count+2 if count>2: return 0 i=i+1 if count==2: return 1 else: return 0 n=int(input()) if n%2==0: for j in range(2,n): s=prime(j) t=pr...
output
1
40,033
22
80,067
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,034
22
80,068
Tags: brute force, math, number theory Correct Solution: ``` import math as m n=int(input()) def prime(n): if n==1: return False for j in range(2,int(m.sqrt(n))+1): if n%j==0: return False return True if prime(n): print(1) print(n) else : ans=[] ans.append(3) ...
output
1
40,034
22
80,069
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,035
22
80,070
Tags: brute force, math, number theory Correct Solution: ``` ######### ## ## ## #### ##### ## # ## # ## # # # # # # # # # # # # # # # # # # # # # # # ### # # # # # # # # # # # # # ##### # # # # ### # # # # # # # # ##### # # ...
output
1
40,035
22
80,071
Provide tags and a correct Python 3 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,036
22
80,072
Tags: brute force, math, number theory Correct Solution: ``` import math n = int(input()) p = [0 for _ in range(1001)] x = 2 p[0] = 1 p[1] = 1 while x * x <= 1001: for i in range(2 * x, 1001, x): p[i] = 1 x += 1 pr = 0 def isprime(num): for i in range(2, int(math.sqrt(n)) + 1): if num % i...
output
1
40,036
22
80,073
Provide tags and a correct Python 2 solution for this coding contest problem. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes. More formally, you are given an odd...
instruction
0
40,037
22
80,074
Tags: brute force, math, number theory Correct Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict from itertools import permutations, combinations raw_input = stdin.readline pr = stdout.write mod=10**9+7 def ni(): return int(raw_input()) def li(): return map(int,raw_inpu...
output
1
40,037
22
80,075
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,038
22
80,076
Yes
output
1
40,038
22
80,077
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,039
22
80,078
Yes
output
1
40,039
22
80,079
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,040
22
80,080
Yes
output
1
40,040
22
80,081
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,041
22
80,082
Yes
output
1
40,041
22
80,083
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,042
22
80,084
No
output
1
40,042
22
80,085
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,043
22
80,086
No
output
1
40,043
22
80,087
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,044
22
80,088
No
output
1
40,044
22
80,089
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr...
instruction
0
40,045
22
80,090
No
output
1
40,045
22
80,091
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an image, that can be represented with a 2-d n by m grid of pixels. Each pixel of the image is either on or off, denoted by the characters "0" or "1", respectively. You would like to compress this image. You want to choose an i...
instruction
0
40,113
22
80,226
Tags: brute force Correct Solution: ``` def debug(*a): return print('[DEBUG]', *a) is_prime = [False, False] + [True] * (2600-2) for i in range(2, 2600): if is_prime[i]: for j in range(i+i, 2600, i): is_prime[j] = False n, m = map(int, input().split()) a = [None] * n for i in range(n):...
output
1
40,113
22
80,227
Provide tags and a correct Python 3 solution for this coding contest problem. You are given an image, that can be represented with a 2-d n by m grid of pixels. Each pixel of the image is either on or off, denoted by the characters "0" or "1", respectively. You would like to compress this image. You want to choose an i...
instruction
0
40,114
22
80,228
Tags: brute force Correct Solution: ``` def debug(*a): return print('[DEBUG]', *a) is_prime = [False, False] + [True] * (2600-2) for i in range(2, 2600): if is_prime[i]: for j in range(i+i, 2600, i): is_prime[j] = False n, m = map(int, input().split()) a = [None] * n for i in range(n):...
output
1
40,114
22
80,229
Provide a correct Python 3 solution for this coding contest problem. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pa...
instruction
0
40,240
22
80,480
"Correct Solution: ``` def modulo_pairing(N: int, M: int, A: list)->int: A.sort() def check(n: int)->bool: '''2*n の位置を区切りとして、右側が全て赤のペアになることを確認する。 ''' for i in range(2*n, N+n): if A[i] + A[2*N+2*n-i-1] < M: return False return True l, r = -1, N+1 ...
output
1
40,240
22
80,481
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,294
22
80,588
"Correct Solution: ``` m=10**9+7;f=max;r=range for _ in r(int(input())): x,y=sorted(map(int,input().split()));s=-1;i=j=1 while j<=x and i+j<=y:i,j,s=j,i+j,s+1 if x<2 or y<3:print(1,x*y%m);continue a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1);i=j=1 for c in r(s): k,l=j,i+j*2 for _ in r(s-c):k,l=l,k+l a+=(y>=k)*f(0,(x-l)...
output
1
40,294
22
80,589
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,295
22
80,590
"Correct Solution: ``` from math import gcd import random,time def gcdcount(n,m): x,y=min(n,m),max(n,m) if x==0: return 0 else: return 1+gcdcount(x,y%x) fibo=[0,1,2] for i in range(100): fibo.append(fibo[-1]+fibo[-2]) gcdfibo=[[],[(1,2)],[(2,3)],[(3,5),(4,7)]] for i in range(4,101): ...
output
1
40,295
22
80,591
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,296
22
80,592
"Correct Solution: ``` m=10**9+7;f=lambda a:max(0,(a-l)//k+1);r=range for _ in r(int(input())): x,y=sorted(map(int,input().split()));s=-1;i=j=k=l=1 while l<=x and k+l<=y:k,l,s=l,k+l,s+1;a=f(y)+f(x) for c in r(s): k,l=j,i+j*2 for _ in r(s-c):k,l=l,k+l a,i,j=a+(y>=k)*f(x)+(x>=k)*f(y),j,i+j if x<2 or y<3:print(1...
output
1
40,296
22
80,593
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,297
22
80,594
"Correct Solution: ``` m=10**9+7 f=lambda x:max(x,0) r=range for _ in r(int(input())): x,y=sorted(map(int,input().split())) s=-1 i=j=1 while j<=x and i+j<=y:i,j,s=j,i+j,s+1 if x==1 or y<3:print(1,x*y%m) else: a=f((y-j)//i+1)+f((x-j)//i+1) i=j=1 for c in r(s): k,l=j,i+j*2 for _ in r(s-c):k,l=l,k+l i...
output
1
40,297
22
80,595
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,298
22
80,596
"Correct Solution: ``` m=10**9+7 f=max r=range for _ in r(int(input())): x,y=sorted(map(int,input().split())) s=-1 i=j=1 while j<=x and i+j<=y:i,j,s=j,i+j,s+1 if x<2 or y<3:print(1,x*y%m);continue else: a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1) i=j=1 for c in r(s): k,l=j,i+j*2 for _ in r(s-c):k,l=l,k+l if ...
output
1
40,298
22
80,597
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,299
22
80,598
"Correct Solution: ``` m=10**9+7 f=max r=range for _ in r(int(input())): x,y=sorted(map(int,input().split())) s=-1 i=j=1 while j<=x and i+j<=y:i,j,s=j,i+j,s+1 if x==1 or y<3:print(1,x*y%m) else: a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1) i=j=1 for c in r(s): k,l=j,i+j*2 for _ in r(s-c):k,l=l,k+l if x>=k:a+=...
output
1
40,299
22
80,599
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,300
22
80,600
"Correct Solution: ``` q=int(input()) m=10**9+7 for _ in range(q): x,y=sorted(map(int,input().split())) s=-1 i=j=1 while j<=x and i+j<=y: i,j=j,i+j s+=1 if x==1 or y<3:print(1,x*y%m) else: a=max(0,(y-j)//i+1)+max(0,(x-j)//i+1) i=j=1 for c in range(s): k,l=j,i+j*2 for _ in range(s-c):k,l=l,k+l i...
output
1
40,300
22
80,601
Provide a correct Python 3 solution for this coding contest problem. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are given Q queries. The i-th query is represented as a pair ...
instruction
0
40,301
22
80,602
"Correct Solution: ``` from math import gcd import random,time def gcdcount(n,m): x,y=min(n,m),max(n,m) if x==0: return 0 else: return 1+gcdcount(x,y%x) fibo=[0,1,2] for i in range(100): fibo.append(fibo[-1]+fibo[-2]) gcdfibo=[[],[(1,2),(1,3)]] for i in range(2,101): temp=[] ...
output
1
40,301
22
80,603
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,302
22
80,604
Yes
output
1
40,302
22
80,605
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,303
22
80,606
Yes
output
1
40,303
22
80,607
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,304
22
80,608
Yes
output
1
40,304
22
80,609
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,305
22
80,610
Yes
output
1
40,305
22
80,611
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,306
22
80,612
No
output
1
40,306
22
80,613
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,307
22
80,614
No
output
1
40,307
22
80,615
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,308
22
80,616
No
output
1
40,308
22
80,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm. You are g...
instruction
0
40,309
22
80,618
No
output
1
40,309
22
80,619
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,599
22
81,198
Yes
output
1
40,599
22
81,199
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,600
22
81,200
Yes
output
1
40,600
22
81,201
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,601
22
81,202
Yes
output
1
40,601
22
81,203
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,602
22
81,204
Yes
output
1
40,602
22
81,205
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,603
22
81,206
No
output
1
40,603
22
81,207
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,604
22
81,208
No
output
1
40,604
22
81,209
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,605
22
81,210
No
output
1
40,605
22
81,211
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given an array a consisting of n positive integers. Initially, you have an integer x = 0. During one move, you can do one of the following two operations: 1. Choose exactly one i fro...
instruction
0
40,606
22
81,212
No
output
1
40,606
22
81,213
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,724
22
81,448
Tags: implementation, math, number theory Correct Solution: ``` def prim_roots(number): if number == 2: return 1 elif number == 4: return 2 z, h = 1, 2 p = list() while h < number: k = pow(h, z, number) while k > 1: z += 1 k = (k * h) % number ...
output
1
40,724
22
81,449
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,725
22
81,450
Tags: implementation, math, number theory Correct Solution: ``` def isPrimitiveRoot(x,p): i = 2 m = phi = p - 1 while i*i <= m: if m%i == 0: if pow(x,phi//i,p) == 1: return 0 while m%i == 0: m //= i i += 1 if m > 1: return pow(x,phi//m,p) != 1 return pow(x,phi,p)...
output
1
40,725
22
81,451
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,726
22
81,452
Tags: implementation, math, number theory Correct Solution: ``` p = int(input()) ans = 0 for i in range(1, p): result = True temp = i for j in range(1, p): if j == p-1: if (temp-1) % p != 0: result = False else: if (temp-1) % p == 0: re...
output
1
40,726
22
81,453
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,727
22
81,454
Tags: implementation, math, number theory Correct Solution: ``` # python 3 """ Modular arithmetic: This has something to do with Extended Euclidean Algorithm """ def cows_and_primitive_roots(p_int): if p_int == 2: return 1 count = 0 for x in range(2, p_int): x_to_i_mod_p = x divisi...
output
1
40,727
22
81,455
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,728
22
81,456
Tags: implementation, math, number theory Correct Solution: ``` p=int(input()) count=0 for i in range(1,p): z,x=1,1 for j in range(1,p-1): x*=i x%=p if x==1: z=0 break if z==1: x*=i x%=p if x==1: count+=1 print(count) ```
output
1
40,728
22
81,457
Provide tags and a correct Python 3 solution for this coding contest problem. The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, comp...
instruction
0
40,729
22
81,458
Tags: implementation, math, number theory Correct Solution: ``` p = int(input()) - 1 def hcf(a, b): if a is 0: return b else: return hcf(b % a, a) cnt = 0 for i in range(1, p + 1): if hcf(i, p) is 1: cnt += 1 print(cnt) ```
output
1
40,729
22
81,459