Add files using upload-large-folder tool

tasks/construct-ae-p38-factorial-factors-l2-s6/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l2-s6/environment/instance.json

@@ -0,0 +1 @@
+{"N": 120, "t": 35, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s6/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [245, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 46, 46, 46, 46, 46, 47, 47, 49, 51, 51, 51, 51, 51, 51, 51, 53, 53, 58, 58, 58, 58, 59, 59, 61, 62, 62, 62, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l2-s6/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l2-s6/tests/instance.json

@@ -0,0 +1 @@
+{"N": 120, "t": 35, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l2-s6/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l2-s6/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p38-factorial-factors-l6-s8/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l6-s8/environment/instance.json

@@ -0,0 +1 @@
+{"N": 8823, "t": 2881, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s8/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [69144, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2881, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2882, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2883, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2884, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2885, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2886, 2887, 2887, 2887, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2888, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2889, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2890, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2891, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2892, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2893, 2894, 2894, 2894, 2894, 2894, 2894, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2895, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2896, 2897, 2897, 2897, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2898, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2899, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2901, 2901, 2901, 2901, 2901, 2901, 2901, 2901, 2901, 2902, 2902, 2902, 2902, 2902, 2902, 2903, 2903, 2903, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2904, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2905, 2906, 2906, 2906, 2906, 2906, 2906, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2908, 2909, 2909, 2909, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2910, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2911, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2912, 2913, 2913, 2913, 2913, 2913, 2913, 2913, 2913, 2913, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2914, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2915, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2916, 2917, 2917, 2917, 2918, 2918, 2918, 2918, 2918, 2918, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2919, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2920, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2921, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2922, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2923, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2924, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2925, 2926, 2926, 2927, 2927, 2927, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2928, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2929, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2930, 2931, 2931, 2931, 2931, 2931, 2931, 2931, 2931, 2931, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2932, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2933, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2934, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2935, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2936, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2937, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2938, 2939, 2939, 2939, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2940, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2941, 2942, 2942, 2942, 2942, 2942, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2943, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2944, 2945, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2946, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2947, 2949, 2949, 2949, 2949, 2949, 2949, 2949, 2949, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2951, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2952, 2953, 2953, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2954, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2955, 2956, 2956, 2956, 2956, 2956, 2956, 2956, 2956, 2956, 2956, 2956, 2957, 2957, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2959, 2961, 2962, 2962, 2962, 2962, 2962, 2963, 2963, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2965, 2966, 2966, 2966, 2966, 2966, 2967, 2969, 2969, 2971, 2971, 2972, 2972, 2972, 2972, 2972, 2972, 2972, 2972, 2972, 2972, 2972, 2973, 2973, 2973, 2973, 2973, 2973, 2973, 2973, 2974, 2974, 2974, 2974, 2974, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2977, 2978, 2978, 2978, 2978, 2978, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2979, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2980, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2981, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2983, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2984, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2985, 2986, 2986, 2986, 2986, 2986, 2989, 2989, 2991, 2991, 2991, 2991, 2991, 2991, 2991, 2991, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2994, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2995, 2997, 2997, 2998, 2998, 2998, 2998, 2998, 2999, 2999, 3001, 3001, 3002, 3004, 3004, 3004, 3004, 3004, 3004, 3004, 3004, 3004, 3004, 3004, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3005, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3006, 3011, 3011, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3012, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3014, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3017, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3018, 3019, 3019, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3020, 3022, 3022, 3022, 3022, 3022, 3023, 3023, 3027, 3027, 3027, 3027, 3027, 3027, 3027, 3027, 3028, 3028, 3028, 3028, 3028, 3028, 3028, 3028, 3028, 3028, 3028, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3029, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3031, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3032, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3033, 3034, 3034, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3035, 3037, 3037, 3039, 3039, 3039, 3039, 3039, 3039, 3039, 3039, 3041, 3041, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3043, 3044, 3044, 3044, 3044, 3044, 3044, 3044, 3044, 3044, 3044, 3044, 3046, 3046, 3046, 3046, 3046, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3047, 3049, 3049, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3054, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3056, 3057, 3057, 3057, 3057, 3057, 3057, 3057, 3057, 3061, 3061, 3062, 3062, 3062, 3062, 3062, 3063, 3063, 3063, 3063, 3063, 3063, 3063, 3063, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3064, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3065, 3067, 3067, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3070, 3072, 3072, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3073, 3076, 3076, 3076, 3076, 3076, 3076, 3076, 3076, 3076, 3076, 3076, 3079, 3079, 3083, 3083, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3084, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3085, 3086, 3086, 3086, 3086, 3086, 3089, 3089, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3091, 3092, 3092, 3092, 3092, 3092, 3092, 3092, 3092, 3092, 3092, 3092, 3093, 3093, 3093, 3093, 3093, 3093, 3093, 3093, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3095, 3098, 3098, 3098, 3098, 3098, 3099, 3099, 3099, 3099, 3099, 3099, 3099, 3099, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3101, 3106, 3106, 3106, 3106, 3106, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3107, 3109, 3109, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3110, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3112, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3113, 3117, 3117, 3117, 3117, 3117, 3117, 3117, 3117, 3118, 3118, 3118, 3118, 3118, 3119, 3119, 3121, 3121, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3134, 3134, 3134, 3134, 3134, 3137, 3137, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3142, 3142, 3142, 3142, 3142, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3147, 3147, 3147, 3147, 3147, 3147, 3147, 3147, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3153, 3153, 3153, 3153, 3153, 3153, 3153, 3153, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3158, 3158, 3158, 3158, 3158, 3163, 3163, 3166, 3166, 3166, 3166, 3166, 3167, 3167, 3169, 3169, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3181, 3181, 3183, 3183, 3183, 3183, 3183, 3183, 3183, 3183, 3187, 3187, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3189, 3189, 3189, 3189, 3189, 3189, 3189, 3189, 3191, 3191, 3194, 3194, 3194, 3194, 3194, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3202, 3202, 3202, 3202, 3202, 3203, 3203, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3207, 3207, 3207, 3207, 3207, 3207, 3207, 3207, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3209, 3209, 3214, 3214, 3214, 3214, 3214, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3217, 3217, 3218, 3218, 3218, 3218, 3218, 3221, 3221, 3226, 3226, 3226, 3226, 3226, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3229, 3229, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3238, 3238, 3238, 3238, 3238, 3239, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3242, 3242, 3242, 3242, 3242, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3247, 3251, 3251, 3253, 3253, 3254, 3254, 3254, 3254, 3254, 3257, 3257, 3259, 3259, 3261, 3261, 3261, 3261, 3261, 3261, 3261, 3261, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3271, 3271, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3273, 3273, 3273, 3273, 3273, 3273, 3273, 3273, 3274, 3274, 3274, 3274, 3274, 3279, 3279, 3279, 3279, 3279, 3279, 3279, 3279, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3287, 3291, 3291, 3291, 3291, 3291, 3291, 3291, 3291, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3299, 3299, 3301, 3301, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3307, 3307, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3309, 3309, 3309, 3309, 3309, 3309, 3309, 3313, 3313, 3314, 3314, 3314, 3314, 3314, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3317, 3319, 3319, 3323, 3323, 3326, 3326, 3326, 3326, 3326, 3327, 3327, 3327, 3327, 3327, 3327, 3327, 3329, 3329, 3331, 3331, 3334, 3334, 3334, 3334, 3334, 3338, 3338, 3338, 3338, 3338, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3343, 3343, 3347, 3347, 3351, 3351, 3351, 3351, 3351, 3351, 3351, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3359, 3359, 3361, 3361, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3369, 3369, 3369, 3369, 3369, 3369, 3369, 3371, 3371, 3373, 3373, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3386, 3386, 3386, 3386, 3386, 3387, 3387, 3387, 3387, 3387, 3387, 3387, 3389, 3389, 3391, 3391, 3394, 3394, 3394, 3394, 3394, 3398, 3398, 3398, 3398, 3398, 3407, 3407, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3413, 3413, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3418, 3418, 3418, 3418, 3418, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3433, 3433, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3442, 3442, 3442, 3442, 3442, 3446, 3446, 3446, 3446, 3446, 3449, 3449, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3453, 3453, 3453, 3453, 3453, 3453, 3453, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3457, 3457, 3459, 3459, 3459, 3459, 3459, 3459, 3459, 3461, 3461, 3463, 3463, 3466, 3466, 3466, 3466, 3466, 3467, 3467, 3469, 3469, 3482, 3482, 3482, 3482, 3482, 3489, 3489, 3489, 3489, 3489, 3489, 3489, 3491, 3491, 3494, 3494, 3494, 3494, 3494, 3499, 3499, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3506, 3506, 3506, 3506, 3506, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3511, 3511, 3513, 3513, 3513, 3513, 3513, 3513, 3513, 3517, 3517, 3518, 3518, 3518, 3518, 3518, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3527, 3527, 3529, 3529, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3533, 3533, 3539, 3539, 3541, 3541, 3543, 3543, 3543, 3543, 3543, 3543, 3543, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3547, 3547, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3554, 3554, 3554, 3554, 3557, 3557, 3559, 3559, 3561, 3561, 3561, 3561, 3561, 3561, 3561, 3566, 3566, 3566, 3566, 3571, 3571, 3574, 3574, 3574, 3574, 3578, 3578, 3578, 3578, 3579, 3579, 3579, 3579, 3579, 3579, 3579, 3581, 3581, 3583, 3583, 3593, 3593, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3602, 3602, 3602, 3602, 3603, 3603, 3603, 3603, 3603, 3603, 3603, 3607, 3607, 3613, 3613, 3617, 3617, 3622, 3622, 3622, 3622, 3623, 3623, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3631, 3631, 3637, 3637, 3639, 3639, 3639, 3639, 3639, 3639, 3639, 3643, 3643, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3646, 3646, 3646, 3646, 3651, 3651, 3651, 3651, 3651, 3651, 3651, 3659, 3659, 3662, 3662, 3662, 3662, 3669, 3669, 3669, 3669, 3669, 3669, 3669, 3671, 3671, 3673, 3673, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3677, 3677, 3687, 3687, 3687, 3687, 3687, 3687, 3687, 3691, 3691, 3693, 3693, 3693, 3693, 3693, 3693, 3693, 3694, 3694, 3694, 3694, 3697, 3697, 3701, 3701, 3709, 3709, 3711, 3711, 3711, 3711, 3711, 3711, 3711, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3719, 3719, 3722, 3722, 3722, 3722, 3727, 3727, 3733, 3733, 3734, 3734, 3734, 3734, 3739, 3739, 3742, 3742, 3742, 3742, 3746, 3746, 3746, 3746, 3747, 3747, 3747, 3747, 3747, 3747, 3747, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3754, 3754, 3754, 3754, 3758, 3758, 3758, 3758, 3761, 3761, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3767, 3767, 3769, 3769, 3777, 3777, 3777, 3777, 3777, 3777, 3777, 3778, 3778, 3778, 3778, 3779, 3779, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3793, 3793, 3797, 3797, 3802, 3802, 3802, 3802, 3803, 3803, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3814, 3814, 3814, 3814, 3821, 3821, 3823, 3823, 3826, 3826, 3826, 3826, 3831, 3831, 3831, 3831, 3831, 3831, 3833, 3833, 3837, 3837, 3837, 3837, 3837, 3837, 3847, 3847, 3849, 3849, 3849, 3849, 3849, 3849, 3851, 3851, 3853, 3853, 3862, 3862, 3862, 3862, 3863, 3863, 3866, 3866, 3866, 3866, 3867, 3867, 3867, 3867, 3867, 3867, 3873, 3873, 3873, 3873, 3873, 3873, 3877, 3877, 3881, 3881, 3889, 3889, 3891, 3891, 3891, 3891, 3891, 3891, 3898, 3898, 3898, 3898, 3902, 3902, 3902, 3902, 3903, 3903, 3903, 3903, 3903, 3903, 3907, 3907, 3909, 3909, 3909, 3909, 3909, 3909, 3911, 3911, 3917, 3917, 3919, 3919, 3921, 3921, 3921, 3921, 3921, 3921, 3923, 3923, 3929, 3929, 3931, 3931, 3943, 3943, 3946, 3946, 3946, 3946, 3947, 3947, 3957, 3957, 3957, 3957, 3957, 3957, 3958, 3958, 3958, 3958, 3963, 3963, 3963, 3963, 3963, 3963, 3967, 3967, 3974, 3974, 3974, 3974, 3981, 3981, 3981, 3981, 3981, 3981, 3986, 3986, 3986, 3986, 3989, 3989, 3994, 3994, 3994, 3994, 3998, 3998, 3998, 3998, 4001, 4001, 4003, 4003, 4006, 4006, 4006, 4006, 4007, 4007, 4013, 4013, 4019, 4019, 4021, 4021, 4022, 4022, 4022, 4022, 4027, 4027, 4034, 4034, 4034, 4034, 4049, 4049, 4051, 4051, 4054, 4054, 4054, 4054, 4057, 4057, 4058, 4058, 4058, 4058, 4073, 4073, 4078, 4078, 4078, 4078, 4079, 4079, 4083, 4083, 4083, 4083, 4083, 4083, 4091, 4091, 4093, 4093, 4099, 4099, 4101, 4101, 4101, 4101, 4101, 4101, 4106, 4106, 4106, 4106, 4111, 4111, 4119, 4119, 4119, 4119, 4119, 4119, 4126, 4126, 4126, 4126, 4127, 4127, 4129, 4129, 4133, 4133, 4138, 4138, 4138, 4138, 4139, 4139, 4143, 4143, 4143, 4143, 4143, 4143, 4153, 4153, 4157, 4157, 4159, 4159, 4162, 4162, 4162, 4162, 4166, 4166, 4166, 4166, 4174, 4174, 4174, 4174, 4177, 4177, 4178, 4178, 4178, 4178, 4197, 4197, 4197, 4197, 4197, 4197, 4198, 4198, 4198, 4198, 4201, 4201, 4211, 4211, 4217, 4217, 4219, 4219, 4222, 4222, 4222, 4222, 4226, 4226, 4226, 4226, 4227, 4227, 4227, 4227, 4227, 4227, 4229, 4229, 4231, 4231, 4241, 4241, 4243, 4243, 4253, 4253, 4258, 4258, 4258, 4258, 4259, 4259, 4261, 4261, 4262, 4262, 4262, 4262, 4269, 4269, 4269, 4269, 4269, 4269, 4271, 4271, 4273, 4273, 4274, 4274, 4274, 4274, 4281, 4281, 4281, 4281, 4281, 4281, 4282, 4282, 4282, 4282, 4283, 4283, 4286, 4286, 4286, 4286, 4287, 4287, 4287, 4287, 4287, 4287, 4289, 4289, 4297, 4297, 4299, 4299, 4299, 4299, 4299, 4299, 4306, 4306, 4306, 4306, 4317, 4317, 4317, 4317, 4317, 4317, 4322, 4322, 4322, 4322, 4327, 4327, 4337, 4337, 4339, 4339, 4349, 4349, 4357, 4357, 4358, 4358, 4358, 4358, 4363, 4363, 4373, 4373, 4391, 4391, 4397, 4397, 4406, 4406, 4406, 4406, 4409, 4409, 4414, 4414, 4414, 4421, 4423, 4426, 4426, 4426, 4441, 4442, 4442, 4442, 4447, 4451, 4457, 4463, 4474, 4474, 4474, 4478, 4478, 4478, 4481, 4483, 4486, 4486, 4486, 4493, 4502, 4502, 4502, 4507, 4513, 4517, 4519, 4523, 4534, 4534, 4534, 4538, 4538, 4538, 4546, 4546, 4546, 4547, 4549, 4561, 4562, 4562, 4562, 4567, 4574, 4574, 4574, 4583, 4586, 4586, 4586, 4591, 4594, 4594, 4594, 4597, 4603, 4618, 4618, 4618, 4621, 4622, 4622, 4622, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4666, 4666, 4666, 4673, 4678, 4678, 4678, 4679, 4682, 4682, 4682, 4691, 4694, 4694, 4694, 4702, 4702, 4702, 4703, 4714, 4714, 4714, 4721, 4723, 4729, 4733, 4742, 4742, 4742, 4751, 4754, 4754, 4754, 4759, 4762, 4762, 4762, 4766, 4766, 4766, 4778, 4778, 4778, 4783, 4786, 4786, 4786, 4787, 4789, 4793, 4798, 4798, 4798, 4799, 4801, 4813, 4817, 4822, 4822, 4822, 4831, 4834, 4834, 4834, 4846, 4846, 4846, 4861, 4871, 4874, 4874, 4874, 4877, 4882, 4882, 4882, 4889, 4894, 4894, 4894, 4903, 4909, 4918, 4918, 4918, 4919, 4931, 4933, 4934, 4934, 4934, 4937, 4943, 4946, 4946, 4946, 4951, 4954, 4954, 4954, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5006, 5006, 5006, 5009, 5011, 5021, 5023, 5039, 5042, 5042, 5042, 5051, 5059, 5062, 5062, 5062, 5077, 5078, 5078, 5078, 5081, 5086, 5086, 5086, 5087, 5098, 5098, 5098, 5099, 5101, 5102, 5102, 5102, 5107, 5113, 5114, 5114, 5114, 5119, 5147, 5153, 5158, 5158, 5158, 5167, 5171, 5179, 5182, 5182, 5182, 5186, 5186, 5186, 5189, 5197, 5209, 5218, 5218, 5218, 5227, 5231, 5233, 5234, 5234, 5234, 5237, 5242, 5242, 5242, 5261, 5266, 5266, 5266, 5273, 5279, 5281, 5294, 5294, 5294, 5297, 5303, 5309, 5314, 5314, 5314, 5318, 5318, 5318, 5323, 5326, 5326, 5326, 5333, 5342, 5342, 5342, 5347, 5351, 5354, 5354, 5354, 5366, 5366, 5366, 5374, 5374, 5374, 5378, 5378, 5378, 5381, 5386, 5386, 5386, 5387, 5393, 5398, 5398, 5398, 5399, 5407, 5413, 5414, 5414, 5414, 5417, 5419, 5422, 5422, 5422, 5426, 5426, 5426, 5431, 5437, 5438, 5438, 5438, 5441, 5443, 5449, 5458, 5458, 5458, 5462, 5462, 5462, 5471, 5477, 5479, 5482, 5482, 5482, 5483, 5498, 5498, 5498, 5501, 5503, 5506, 5506, 5506, 5507, 5519, 5521, 5527, 5531, 5534, 5534, 5534, 5554, 5554, 5554, 5557, 5563, 5569, 5573, 5578, 5578, 5578, 5581, 5582, 5582, 5582, 5591, 5594, 5594, 5594, 5602, 5602, 5602, 5606, 5606, 5606, 5623, 5638, 5638, 5638, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5666, 5666, 5666, 5669, 5674, 5674, 5674, 5683, 5686, 5686, 5686, 5689, 5693, 5701, 5702, 5702, 5702, 5711, 5714, 5714, 5714, 5717, 5722, 5722, 5722, 5737, 5741, 5743, 5749, 5758, 5758, 5758, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l6-s8/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l6-s8/tests/instance.json

@@ -0,0 +1 @@
+{"N": 8823, "t": 2881, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s8/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l6-s8/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p38-factorial-factors-l6-s9/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p38-factorial-factors-l6-s9/environment/instance.json

@@ -0,0 +1 @@
+{"N": 9545, "t": 3118, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s9/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [18708, 3118, 3118, 3118, 3118, 3118, 3119, 3119, 3119, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3121, 3121, 3121, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3122, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3123, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3124, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3126, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3127, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3128, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3129, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3130, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3131, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3132, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3133, 3134, 3134, 3134, 3134, 3134, 3134, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3135, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3136, 3137, 3137, 3137, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3138, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3139, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3140, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3141, 3142, 3142, 3142, 3142, 3142, 3142, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3143, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3144, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3145, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3146, 3147, 3147, 3147, 3147, 3147, 3147, 3147, 3147, 3147, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3148, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3149, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3151, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3152, 3153, 3153, 3153, 3153, 3153, 3153, 3153, 3153, 3153, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3154, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3155, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3156, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3157, 3158, 3158, 3158, 3158, 3158, 3158, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3159, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3160, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3161, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3162, 3163, 3163, 3163, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3164, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3165, 3166, 3166, 3166, 3166, 3166, 3166, 3167, 3167, 3167, 3169, 3169, 3169, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3171, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3172, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3173, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3174, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3175, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3176, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3177, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3178, 3179, 3179, 3181, 3181, 3181, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3182, 3183, 3183, 3183, 3183, 3183, 3183, 3183, 3183, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3184, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3185, 3187, 3187, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3188, 3189, 3189, 3189, 3189, 3189, 3189, 3189, 3189, 3191, 3191, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3193, 3194, 3194, 3194, 3194, 3194, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3197, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3199, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3201, 3202, 3202, 3202, 3202, 3202, 3203, 3203, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3204, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3205, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3206, 3207, 3207, 3207, 3207, 3207, 3207, 3207, 3207, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3208, 3209, 3209, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3210, 3211, 3214, 3214, 3214, 3214, 3214, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3215, 3217, 3217, 3218, 3218, 3218, 3218, 3218, 3221, 3221, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3222, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3223, 3226, 3226, 3226, 3226, 3226, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3227, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3228, 3229, 3229, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3231, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3233, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3235, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3236, 3238, 3238, 3238, 3238, 3238, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3241, 3242, 3242, 3242, 3242, 3242, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3243, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3244, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3246, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3247, 3251, 3251, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3252, 3253, 3253, 3254, 3254, 3254, 3254, 3254, 3257, 3257, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3258, 3259, 3259, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3260, 3261, 3261, 3261, 3261, 3261, 3261, 3261, 3261, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3262, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3263, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3265, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3269, 3271, 3271, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3272, 3273, 3273, 3273, 3273, 3273, 3273, 3273, 3273, 3274, 3274, 3274, 3274, 3274, 3279, 3279, 3279, 3279, 3279, 3279, 3279, 3279, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3281, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3282, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3284, 3286, 3286, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3287, 3291, 3291, 3291, 3291, 3291, 3291, 3291, 3291, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3292, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3295, 3299, 3299, 3301, 3301, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3303, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3305, 3307, 3307, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3308, 3309, 3309, 3309, 3309, 3309, 3309, 3309, 3309, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3310, 3313, 3313, 3314, 3314, 3314, 3314, 3314, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3316, 3319, 3319, 3323, 3323, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3324, 3326, 3326, 3326, 3326, 3326, 3327, 3327, 3327, 3327, 3327, 3327, 3327, 3327, 3329, 3329, 3331, 3331, 3334, 3334, 3334, 3334, 3334, 3338, 3338, 3338, 3338, 3338, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3341, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3342, 3343, 3343, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3346, 3347, 3347, 3351, 3351, 3351, 3351, 3351, 3351, 3351, 3351, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3352, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3353, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3356, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3357, 3359, 3359, 3361, 3361, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3365, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3368, 3369, 3369, 3369, 3369, 3369, 3369, 3369, 3369, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3370, 3371, 3371, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3372, 3373, 3373, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3377, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3378, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3386, 3386, 3386, 3386, 3386, 3387, 3387, 3387, 3387, 3387, 3387, 3387, 3387, 3389, 3389, 3391, 3391, 3394, 3394, 3394, 3394, 3394, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3396, 3398, 3398, 3398, 3398, 3398, 3407, 3407, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3409, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3411, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3412, 3413, 3413, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3414, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3415, 3418, 3418, 3418, 3418, 3418, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3421, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3426, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3428, 3429, 3433, 3433, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3436, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3437, 3442, 3442, 3442, 3442, 3442, 3446, 3446, 3446, 3446, 3446, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3447, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3448, 3449, 3449, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3452, 3453, 3453, 3453, 3453, 3453, 3453, 3453, 3453, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3455, 3457, 3457, 3459, 3459, 3459, 3459, 3459, 3459, 3459, 3459, 3461, 3461, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3462, 3463, 3463, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3464, 3466, 3466, 3466, 3466, 3466, 3467, 3467, 3469, 3469, 3482, 3482, 3482, 3482, 3482, 3489, 3489, 3489, 3489, 3489, 3489, 3489, 3489, 3491, 3491, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3493, 3494, 3494, 3494, 3494, 3494, 3499, 3499, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3501, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3505, 3506, 3506, 3506, 3506, 3506, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3508, 3511, 3511, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3512, 3513, 3513, 3513, 3513, 3513, 3513, 3513, 3513, 3517, 3517, 3518, 3518, 3518, 3518, 3518, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3521, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3522, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3524, 3527, 3527, 3529, 3529, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3532, 3533, 3533, 3539, 3539, 3541, 3541, 3543, 3543, 3543, 3543, 3543, 3543, 3543, 3543, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3544, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3545, 3547, 3547, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3548, 3554, 3554, 3554, 3554, 3554, 3557, 3557, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3558, 3559, 3559, 3561, 3561, 3561, 3561, 3561, 3561, 3561, 3561, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3563, 3566, 3566, 3566, 3566, 3566, 3571, 3571, 3574, 3574, 3574, 3574, 3574, 3578, 3578, 3578, 3578, 3578, 3579, 3579, 3579, 3579, 3579, 3579, 3579, 3579, 3581, 3581, 3583, 3583, 3593, 3593, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3594, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3595, 3602, 3602, 3602, 3602, 3602, 3603, 3603, 3603, 3603, 3603, 3603, 3603, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3606, 3607, 3607, 3613, 3613, 3617, 3617, 3622, 3622, 3622, 3622, 3622, 3623, 3623, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3628, 3631, 3631, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3635, 3637, 3637, 3639, 3639, 3639, 3639, 3639, 3639, 3639, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3642, 3643, 3643, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3644, 3646, 3646, 3646, 3646, 3646, 3651, 3651, 3651, 3651, 3651, 3651, 3651, 3659, 3659, 3662, 3662, 3662, 3662, 3662, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3665, 3669, 3669, 3669, 3669, 3669, 3669, 3669, 3671, 3671, 3673, 3673, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3676, 3677, 3677, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3678, 3687, 3687, 3687, 3687, 3687, 3687, 3687, 3691, 3691, 3693, 3693, 3693, 3693, 3693, 3693, 3693, 3694, 3694, 3694, 3694, 3694, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3695, 3697, 3697, 3701, 3701, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3702, 3709, 3709, 3711, 3711, 3711, 3711, 3711, 3711, 3711, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3714, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3715, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3716, 3719, 3719, 3722, 3722, 3722, 3722, 3722, 3727, 3727, 3733, 3733, 3734, 3734, 3734, 3734, 3734, 3739, 3739, 3742, 3742, 3742, 3742, 3742, 3746, 3746, 3746, 3746, 3746, 3747, 3747, 3747, 3747, 3747, 3747, 3747, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3748, 3754, 3754, 3754, 3754, 3754, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3755, 3758, 3758, 3758, 3758, 3758, 3761, 3761, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3764, 3767, 3767, 3769, 3769, 3777, 3777, 3777, 3777, 3777, 3777, 3777, 3778, 3778, 3778, 3778, 3778, 3779, 3779, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3785, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3788, 3793, 3793, 3797, 3797, 3802, 3802, 3802, 3802, 3802, 3803, 3803, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3805, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3812, 3814, 3814, 3814, 3814, 3814, 3821, 3821, 3823, 3823, 3826, 3826, 3826, 3826, 3831, 3831, 3831, 3831, 3831, 3831, 3831, 3833, 3833, 3837, 3837, 3837, 3837, 3837, 3837, 3837, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3845, 3847, 3847, 3849, 3849, 3849, 3849, 3849, 3849, 3849, 3851, 3851, 3853, 3853, 3862, 3862, 3862, 3862, 3863, 3863, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3865, 3866, 3866, 3866, 3866, 3867, 3867, 3867, 3867, 3867, 3867, 3867, 3868, 3868, 3868, 3868, 3868, 3868, 3868, 3868, 3868, 3873, 3873, 3873, 3873, 3873, 3873, 3873, 3877, 3877, 3881, 3881, 3884, 3884, 3884, 3884, 3884, 3884, 3884, 3884, 3884, 3889, 3889, 3891, 3891, 3891, 3891, 3891, 3891, 3891, 3898, 3898, 3898, 3898, 3902, 3902, 3902, 3902, 3903, 3903, 3903, 3903, 3903, 3903, 3903, 3907, 3907, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3908, 3909, 3909, 3909, 3909, 3909, 3909, 3909, 3911, 3911, 3917, 3917, 3919, 3919, 3921, 3921, 3921, 3921, 3921, 3921, 3921, 3923, 3923, 3929, 3929, 3931, 3931, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3932, 3943, 3943, 3946, 3946, 3946, 3946, 3947, 3947, 3957, 3957, 3957, 3957, 3957, 3957, 3957, 3958, 3958, 3958, 3958, 3963, 3963, 3963, 3963, 3963, 3963, 3963, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3964, 3967, 3967, 3974, 3974, 3974, 3974, 3981, 3981, 3981, 3981, 3981, 3981, 3981, 3986, 3986, 3986, 3986, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3988, 3989, 3989, 3994, 3994, 3994, 3994, 3998, 3998, 3998, 3998, 4001, 4001, 4003, 4003, 4006, 4006, 4006, 4006, 4007, 4007, 4013, 4013, 4019, 4019, 4021, 4021, 4022, 4022, 4022, 4022, 4027, 4027, 4034, 4034, 4034, 4034, 4036, 4036, 4036, 4036, 4036, 4036, 4036, 4036, 4036, 4049, 4049, 4051, 4051, 4052, 4052, 4052, 4052, 4052, 4052, 4052, 4052, 4052, 4054, 4054, 4054, 4054, 4057, 4057, 4058, 4058, 4058, 4058, 4073, 4073, 4076, 4076, 4076, 4076, 4076, 4076, 4076, 4076, 4076, 4078, 4078, 4078, 4078, 4079, 4079, 4083, 4083, 4083, 4083, 4083, 4083, 4083, 4084, 4084, 4084, 4084, 4084, 4084, 4084, 4084, 4084, 4091, 4091, 4093, 4093, 4099, 4099, 4101, 4101, 4101, 4101, 4101, 4101, 4106, 4106, 4106, 4106, 4111, 4111, 4119, 4119, 4119, 4119, 4119, 4119, 4124, 4124, 4124, 4124, 4124, 4124, 4124, 4124, 4124, 4126, 4126, 4126, 4126, 4127, 4127, 4129, 4129, 4132, 4132, 4132, 4132, 4132, 4132, 4132, 4132, 4132, 4133, 4133, 4138, 4138, 4138, 4138, 4139, 4139, 4143, 4143, 4143, 4143, 4143, 4143, 4153, 4153, 4156, 4156, 4156, 4156, 4156, 4156, 4156, 4156, 4156, 4157, 4157, 4159, 4159, 4162, 4162, 4162, 4162, 4166, 4166, 4166, 4166, 4174, 4174, 4174, 4174, 4177, 4177, 4178, 4178, 4178, 4178, 4197, 4197, 4197, 4197, 4197, 4197, 4198, 4198, 4198, 4198, 4201, 4201, 4211, 4211, 4217, 4217, 4219, 4219, 4222, 4222, 4222, 4222, 4226, 4226, 4226, 4226, 4227, 4227, 4227, 4227, 4227, 4227, 4229, 4229, 4231, 4231, 4241, 4241, 4243, 4243, 4253, 4253, 4258, 4258, 4258, 4258, 4259, 4259, 4261, 4261, 4262, 4262, 4262, 4262, 4269, 4269, 4269, 4269, 4269, 4269, 4271, 4271, 4273, 4273, 4274, 4274, 4274, 4274, 4281, 4281, 4281, 4281, 4281, 4281, 4282, 4282, 4282, 4282, 4283, 4283, 4286, 4286, 4286, 4286, 4287, 4287, 4287, 4287, 4287, 4287, 4289, 4289, 4297, 4297, 4299, 4299, 4299, 4299, 4299, 4299, 4306, 4306, 4306, 4306, 4317, 4317, 4317, 4317, 4317, 4317, 4322, 4322, 4322, 4322, 4327, 4327, 4337, 4337, 4339, 4339, 4341, 4341, 4341, 4341, 4341, 4341, 4349, 4349, 4353, 4353, 4353, 4353, 4353, 4353, 4357, 4357, 4358, 4358, 4358, 4358, 4359, 4359, 4359, 4359, 4359, 4359, 4363, 4363, 4373, 4373, 4377, 4377, 4377, 4377, 4377, 4377, 4391, 4391, 4397, 4397, 4406, 4406, 4406, 4406, 4409, 4409, 4413, 4413, 4413, 4413, 4413, 4413, 4414, 4414, 4414, 4414, 4421, 4421, 4423, 4423, 4426, 4426, 4426, 4426, 4441, 4441, 4442, 4442, 4442, 4442, 4443, 4443, 4443, 4443, 4443, 4443, 4447, 4447, 4449, 4449, 4449, 4449, 4449, 4449, 4451, 4451, 4457, 4457, 4461, 4461, 4461, 4461, 4461, 4461, 4463, 4463, 4467, 4467, 4467, 4467, 4467, 4467, 4474, 4474, 4474, 4474, 4478, 4478, 4478, 4478, 4479, 4479, 4479, 4479, 4479, 4479, 4481, 4481, 4483, 4483, 4486, 4486, 4486, 4486, 4493, 4493, 4497, 4497, 4497, 4497, 4497, 4497, 4502, 4502, 4502, 4502, 4507, 4507, 4513, 4513, 4517, 4517, 4519, 4519, 4523, 4523, 4533, 4533, 4533, 4533, 4533, 4533, 4534, 4534, 4534, 4534, 4538, 4538, 4538, 4538, 4546, 4546, 4546, 4546, 4547, 4547, 4549, 4549, 4561, 4561, 4562, 4562, 4562, 4562, 4567, 4567, 4569, 4569, 4569, 4569, 4569, 4569, 4574, 4574, 4574, 4574, 4583, 4583, 4586, 4586, 4586, 4586, 4591, 4591, 4593, 4593, 4593, 4593, 4593, 4593, 4594, 4594, 4594, 4594, 4597, 4597, 4603, 4603, 4618, 4618, 4618, 4618, 4621, 4621, 4622, 4622, 4622, 4622, 4629, 4629, 4629, 4629, 4629, 4629, 4637, 4637, 4639, 4639, 4643, 4643, 4647, 4647, 4647, 4647, 4647, 4647, 4649, 4649, 4651, 4651, 4657, 4657, 4659, 4659, 4659, 4659, 4659, 4659, 4663, 4663, 4666, 4666, 4666, 4666, 4673, 4673, 4678, 4678, 4678, 4678, 4679, 4679, 4682, 4682, 4682, 4682, 4691, 4691, 4694, 4694, 4694, 4694, 4702, 4702, 4702, 4702, 4703, 4703, 4714, 4714, 4714, 4714, 4721, 4721, 4723, 4723, 4729, 4729, 4733, 4733, 4742, 4742, 4742, 4742, 4751, 4751, 4754, 4754, 4754, 4754, 4759, 4759, 4762, 4762, 4762, 4762, 4766, 4766, 4766, 4766, 4778, 4778, 4778, 4783, 4786, 4786, 4786, 4787, 4789, 4793, 4798, 4798, 4798, 4799, 4801, 4813, 4817, 4822, 4822, 4822, 4831, 4834, 4834, 4834, 4846, 4846, 4846, 4861, 4871, 4874, 4874, 4874, 4877, 4882, 4882, 4882, 4889, 4894, 4894, 4894, 4903, 4909, 4918, 4918, 4918, 4919, 4931, 4933, 4934, 4934, 4934, 4937, 4943, 4946, 4946, 4946, 4951, 4954, 4954, 4954, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5006, 5006, 5006, 5009, 5011, 5021, 5023, 5039, 5042, 5042, 5042, 5051, 5059, 5062, 5062, 5062, 5077, 5078, 5078, 5078, 5081, 5086, 5086, 5086, 5087, 5098, 5098, 5098, 5099, 5101, 5102, 5102, 5102, 5107, 5113, 5114, 5114, 5114, 5119, 5147, 5153, 5158, 5158, 5158, 5167, 5171, 5179, 5182, 5182, 5182, 5186, 5186, 5186, 5189, 5197, 5209, 5218, 5218, 5218, 5227, 5231, 5233, 5234, 5234, 5234, 5237, 5242, 5242, 5242, 5261, 5266, 5266, 5266, 5273, 5279, 5281, 5294, 5294, 5294, 5297, 5303, 5309, 5314, 5314, 5314, 5318, 5318, 5318, 5323, 5326, 5326, 5326, 5333, 5342, 5342, 5342, 5347, 5351, 5354, 5354, 5354, 5366, 5366, 5366, 5374, 5374, 5374, 5378, 5378, 5378, 5381, 5386, 5386, 5386, 5387, 5393, 5398, 5398, 5398, 5399, 5407, 5413, 5414, 5414, 5414, 5417, 5419, 5422, 5422, 5422, 5426, 5426, 5426, 5431, 5437, 5438, 5438, 5438, 5441, 5443, 5449, 5458, 5458, 5458, 5462, 5462, 5462, 5471, 5477, 5479, 5482, 5482, 5482, 5483, 5498, 5498, 5498, 5501, 5503, 5506, 5506, 5506, 5507, 5519, 5521, 5527, 5531, 5534, 5534, 5534, 5554, 5554, 5554, 5557, 5563, 5569, 5573, 5578, 5578, 5578, 5581, 5582, 5582, 5582, 5591, 5594, 5594, 5594, 5602, 5602, 5602, 5606, 5606, 5606, 5623, 5638, 5638, 5638, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5666, 5666, 5666, 5669, 5674, 5674, 5674, 5683, 5686, 5686, 5686, 5689, 5693, 5701, 5702, 5702, 5702, 5711, 5714, 5714, 5714, 5717, 5722, 5722, 5722, 5737, 5741, 5743, 5749, 5758, 5758, 5758, 5774, 5774, 5774, 5779, 5783, 5791, 5794, 5794, 5794, 5801, 5806, 5806, 5806, 5807, 5813, 5818, 5818, 5818, 5821, 5827, 5834, 5834, 5834, 5839, 5843, 5849, 5851, 5854, 5854, 5854, 5857, 5861, 5867, 5869, 5878, 5878, 5878, 5879, 5881, 5897, 5903, 5906, 5906, 5906, 5914, 5914, 5914, 5923, 5926, 5926, 5926, 5927, 5938, 5938, 5938, 5939, 5942, 5942, 5942, 5953, 5981, 5987, 5998, 5998, 5998, 6002, 6002, 6002, 6007, 6011, 6022, 6022, 6022, 6029, 6037, 6038, 6038, 6038, 6043, 6046, 6046, 6046, 6047, 6053, 6067, 6073, 6074, 6074, 6074, 6079, 6082, 6082, 6082, 6089, 6091, 6098, 6098, 6098, 6101, 6113, 6121, 6122, 6122, 6122, 6131, 6133, 6134, 6134, 6134, 6143, 6151, 6158, 6158, 6158, 6163, 6166, 6166, 6166, 6173, 6178, 6178, 6178, 6197, 6199, 6203, 6211, 6217, 6218, 6218, 6218, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539]}
+RLMATH_EOF

tasks/construct-ae-p38-factorial-factors-l6-s9/tests/check.py

@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}

tasks/construct-ae-p38-factorial-factors-l6-s9/tests/instance.json

@@ -0,0 +1 @@
+{"N": 9545, "t": 3118, "family": "ae_p38_factorial_factors", "subset": "construct"}

tasks/construct-ae-p38-factorial-factors-l6-s9/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p38-factorial-factors-l6-s9/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-ae-p58-happy-ending-l1-s0/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-ae-p58-happy-ending-l1-s0/environment/instance.json

@@ -0,0 +1 @@
+{"n": 8, "k": 5, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"}

tasks/construct-ae-p58-happy-ending-l1-s0/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"points": [[0, 0], [15000, -15000000], [15001, -14999998], [15002, -14999990], [30000, -60000000], [30001, -59999990], [30002, -59999988], [45000, -135000000]]}
+RLMATH_EOF

tasks/construct-ae-p58-happy-ending-l1-s0/tests/check.py

@@ -0,0 +1,69 @@
+"""Erdos-Szekeres happy ending (AlphaEvolve problem 58): n = 2^(k-2) integer points in general position with no
+k points in convex position. Exact integer orientation tests; the largest convex-position subset is computed by
+the O(n^4) bottom-vertex / angular-order dynamic programme.
+
+Upstream bug: the notebook's verifier uses float orientations with a 1e-9 threshold (and numba fastmath); its
+33- and 65-point sets (claimed to have "0 convex k-gons") contain a convex 7-gon / 8-gon under exact arithmetic."""
+import functools
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def orient_table(p):
+    n = len(p)
+    o = np.zeros((n, n, n), dtype=np.int8)
+    for i in range(n):
+        xi, yi = p[i]
+        for j in range(i + 1, n):
+            dx, dy = p[j][0] - xi, p[j][1] - yi
+            for k in range(j + 1, n):
+                c = dx * (p[k][1] - yi) - dy * (p[k][0] - xi)
+                if c == 0:
+                    raise Invalid(f"points {p[i]}, {p[j]}, {p[k]} are collinear")
+                s = 1 if c > 0 else -1
+                o[i, j, k] = o[j, k, i] = o[k, i, j] = s
+                o[i, k, j] = o[k, j, i] = o[j, i, k] = -s
+    return o
+
+
+def max_convex(p, o):
+    n = len(p)
+    best = min(n, 3)
+    order = sorted(range(n), key=lambda i: (p[i][1], p[i][0]))
+    for bi, b in enumerate(order):
+        rest = order[bi + 1:]
+        m = len(rest)
+        if m < 2:
+            continue
+        rest = sorted(rest, key=functools.cmp_to_key(lambda u, v: -int(o[b, u, v])))
+        r = np.array(rest)
+        chain = np.zeros((m, m), dtype=np.int32)  # chain[i, j]: longest convex chain b .. r_i -> r_j
+        for j in range(1, m):
+            for i in range(j):
+                v = 3
+                if i > 0:
+                    ok = (chain[:i, i] > 0) & (o[r[:i], r[i], r[j]] > 0)
+                    if ok.any():
+                        v = max(v, int(chain[:i, i][ok].max()) + 1)
+                chain[i, j] = v
+            close = o[r[:j], r[j], b] > 0
+            if close.any():
+                best = max(best, int(chain[:j, j][close].max()))
+    return best
+
+
+def check(inst, ans):
+    n, k, lim = inst["n"], inst["k"], inst["max_abs"]
+    pts = ans.get("points")
+    if not isinstance(pts, list) or len(pts) != n:
+        raise Invalid(f"points must be a list of {n} [x, y] pairs")
+    p = [tuple(int_list(q, 2, -lim, lim, "point")) for q in pts]
+    if len(set(p)) != n:
+        raise Invalid("points must be distinct")
+    o = orient_table(p)
+    mc = max_convex(p, o)
+    if mc >= k:
+        raise Invalid(f"the set contains {mc} points in convex position (>= {k})")
+    return None, {"max_convex_subset": mc}

tasks/construct-ae-p58-happy-ending-l1-s0/tests/instance.json

@@ -0,0 +1 @@
+{"n": 8, "k": 5, "max_abs": 1000000000000000000, "family": "ae_p58_happy_ending", "subset": "construct"}

tasks/construct-ae-p58-happy-ending-l1-s0/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-ae-p58-happy-ending-l1-s0/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-mc-all-interval-l6-s0/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-mc-all-interval-l6-s0/environment/instance.json

@@ -0,0 +1 @@
+{"n": 72, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-interval-l6-s0/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 71, 1, 70, 2, 69, 3, 68, 4, 67, 5, 66, 6, 65, 7, 64, 8, 63, 9, 62, 10, 61, 11, 60, 12, 59, 13, 58, 14, 57, 15, 56, 16, 55, 17, 54, 18, 53, 19, 52, 20, 51, 21, 50, 22, 49, 23, 48, 24, 47, 25, 46, 26, 45, 27, 44, 28, 43, 29, 42, 30, 41, 31, 40, 32, 39, 33, 38, 34, 37, 35, 36]}
+RLMATH_EOF

tasks/construct-mc-all-interval-l6-s0/tests/check.py

@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}

tasks/construct-mc-all-interval-l6-s0/tests/instance.json

@@ -0,0 +1 @@
+{"n": 72, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-interval-l6-s0/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-mc-all-interval-l6-s7/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-mc-all-interval-l6-s7/environment/instance.json

@@ -0,0 +1 @@
+{"n": 120, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-interval-l6-s7/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 119, 1, 118, 2, 117, 3, 116, 4, 115, 5, 114, 6, 113, 7, 112, 8, 111, 9, 110, 10, 109, 11, 108, 12, 107, 13, 106, 14, 105, 15, 104, 16, 103, 17, 102, 18, 101, 19, 100, 20, 99, 21, 98, 22, 97, 23, 96, 24, 95, 25, 94, 26, 93, 27, 92, 28, 91, 29, 90, 30, 89, 31, 88, 32, 87, 33, 86, 34, 85, 35, 84, 36, 83, 37, 82, 38, 81, 39, 80, 40, 79, 41, 78, 42, 77, 43, 76, 44, 75, 45, 74, 46, 73, 47, 72, 48, 71, 49, 70, 50, 69, 51, 68, 52, 67, 53, 66, 54, 65, 55, 64, 56, 63, 57, 62, 58, 61, 59, 60]}
+RLMATH_EOF

tasks/construct-mc-all-interval-l6-s7/tests/check.py

@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}

tasks/construct-mc-all-interval-l6-s7/tests/instance.json

@@ -0,0 +1 @@
+{"n": 120, "fixed": [], "family": "mc_all_interval", "subset": "construct"}

tasks/construct-mc-all-interval-l6-s7/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-mc-all-interval-l6-s7/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-mc-bibd-l5-s3/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-mc-bibd-l5-s3/environment/instance.json

@@ -0,0 +1 @@
+{"v": 18, "k": 3, "lambda": 2, "b": 102, "family": "mc_bibd", "subset": "construct"}

tasks/construct-mc-bibd-l5-s3/solution/solve.sh

@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"blocks": [[4, 15, 16], [3, 13, 14], [0, 3, 7], [4, 5, 13], [5, 10, 17], [4, 7, 10], [6, 16, 17], [3, 4, 17], [0, 4, 10], [1, 10, 16], [1, 13, 17], [2, 7, 10], [10, 12, 16], [11, 13, 15], [8, 13, 17], [1, 4, 9], [0, 4, 16], [6, 7, 11], [4, 8, 12], [5, 11, 16], [4, 8, 15], [1, 2, 11], [2, 4, 13], [2, 6, 17], [1, 2, 16], [11, 14, 17], [4, 6, 11], [1, 3, 4], [3, 6, 13], [1, 14, 15], [1, 3, 12], [1, 12, 13], [0, 12, 17], [0, 3, 17], [1, 5, 7], [1, 5, 6], [5, 12, 13], [7, 13, 15], [1, 6, 8], [7, 8, 11], [1, 7, 8], [8, 9, 12], [1, 9, 17], [0, 1, 14], [6, 9, 15], [3, 6, 7], [3, 10, 15], [3, 5, 9], [3, 9, 11], [9, 12, 15], [9, 13, 16], [0, 13, 16], [0, 10, 14], [2, 7, 12], [6, 10, 13], [10, 11, 12], [8, 10, 15], [6, 12, 15], [1, 10, 11], [6, 8, 14], [3, 8, 16], [11, 12, 16], [11, 15, 17], [2, 6, 16], [2, 3, 8], [3, 15, 16], [8, 14, 16], [7, 13, 14], [0, 11, 13], [0, 6, 12], [8, 9, 11], [0, 5, 11], [6, 10, 14], [0, 1, 15], [7, 15, 17], [7, 12, 14], [5, 14, 15], [3, 5, 10], [3, 12, 14], [5, 7, 16], [4, 7, 9], [5, 9, 14], [4, 5, 6], [9, 14, 16], [0, 7, 9], [0, 2, 15], [0, 2, 8], [2, 14, 17], [5, 8, 17], [7, 16, 17], [4, 11, 14], [0, 6, 9], [2, 4, 14], [2, 5, 12], [8, 10, 13], [2, 9, 13], [9, 10, 17], [0, 5, 8], [4, 12, 17], [2, 9, 10], [2, 5, 15], [2, 3, 11]]}
+RLMATH_EOF

tasks/construct-mc-bibd-l5-s3/tests/check.py

@@ -0,0 +1,25 @@
+"""Balanced incomplete block design BIBD(v, k, lambda) (MathConstraint bibd, CC-BY-4.0).
+Answer = list of b blocks; every block is a k-subset of {0..v-1}, every pair of points lies in exactly
+lambda blocks (which forces every point to lie in r blocks). Repeated blocks are allowed, as upstream
+(its 0/1 incidence-matrix model does not forbid equal columns)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    v, k, lam, b = inst["v"], inst["k"], inst["lambda"], inst["b"]
+    blocks = ans.get("blocks")
+    if not isinstance(blocks, list) or len(blocks) != b:
+        raise Invalid(f"blocks must be a list of exactly {b} blocks")
+    pair = {}
+    for B in blocks:
+        B = int_list(B, k, 0, v - 1, "block")
+        if len(set(B)) != k:
+            raise Invalid("a block contains a repeated point")
+        for p in itertools.combinations(sorted(B), 2):
+            pair[p] = pair.get(p, 0) + 1
+    for p in itertools.combinations(range(v), 2):
+        if pair.get(p, 0) != lam:
+            raise Invalid(f"points {p} lie together in {pair.get(p, 0)} blocks, need {lam}")
+    return None, {}

tasks/construct-mc-bibd-l5-s3/tests/instance.json

@@ -0,0 +1 @@
+{"v": 18, "k": 3, "lambda": 2, "b": 102, "family": "mc_bibd", "subset": "construct"}

tasks/construct-mc-bibd-l5-s3/tests/run.py

@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()

tasks/construct-mc-bibd-l5-s3/tests/test.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt

tasks/construct-mc-bibd-l5-s4/environment/Dockerfile

@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json

tasks/construct-mc-bibd-l5-s4/environment/instance.json

@@ -0,0 +1 @@
+{"v": 23, "k": 11, "lambda": 5, "b": 23, "family": "mc_bibd", "subset": "construct"}