"""Independent admissibility check of a k-tuple file (one integer per line, or comma/space separated).
A tuple h_1<...<h_k is admissible iff for every prime p <= k the residues h_i mod p miss some class
(for p > k this is automatic).  Reports k, diameter, and the verdict."""
import sys, re, json
import numpy as np
def primes_upto(n):
    s = np.ones(n + 1, bool); s[:2] = False
    for p in range(2, int(n ** 0.5) + 1):
        if s[p]:
            s[p * p::p] = False
    return np.nonzero(s)[0]
def check(t):
    t = np.unique(np.asarray(t, dtype=np.int64))
    k = len(t)
    for p in primes_upto(max(k, 2)):
        r = np.bincount((t % p).astype(np.int64), minlength=int(p))
        if r.min() > 0:
            return dict(k=k, diameter=int(t[-1] - t[0]), admissible=False, bad_prime=int(p))
    return dict(k=k, diameter=int(t[-1] - t[0]), admissible=True)
if __name__ == "__main__":
    for f in sys.argv[1:]:
        if f.endswith(".npy"):
            t = np.load(f)
        else:
            t = [int(x) for x in re.findall(r"-?\d+", open(f).read())]
        out = check(t); out["file"] = f.split("/")[-1]
        print(json.dumps(out), flush=True)