"""Independent finite sanity check; not a universal proof. Standard library only."""
from collections import Counter
from math import gcd
import json

rows = []
for q in range(1, 33):
    n = 4*q
    units = [u for u in range(n) if gcd(u,n)==1]
    for x in range(n):
        if x in (0,q,2*q,3*q):
            continue
        p = {0,q,x,(x+2*q)%n}
        target = {0,q,(x+q)%n,(x+3*q)%n}
        profile = lambda s: Counter((a+b)%n for a in s for b in s)
        assert len(p)==len(target)==4
        assert profile(p)==profile(target), (q,x,'profile')
        # Exhaust all unit multipliers. Since 0 is in p, any admissible offset
        # must lie in target. No use of the four-system classification here.
        witness = next(((u,v) for u in units for v in target
                        if {(u*a+v)%n for a in p}==target), None)
        predicted_nonaffine = (q//gcd(q,x))%4==2
        assert (witness is None)==predicted_nonaffine, (q,x,witness)
        rows.append({'q':q,'x':x,'nonaffine':predicted_nonaffine})
result = {'q_max':32,'admissible_parameters':len(rows),
          'nonaffine_parameters':sum(r['nonaffine'] for r in rows),
          'profile_mismatches':0,'criterion_mismatches':0,
          'method':'all units and all possible offsets; exact integer counts'}
print(json.dumps(result,indent=2))