FA-15326 / Numerics / Open access

Involution permutations: transposition partner coverage · case 01

The exact involution permutations result violates the stated contract at transposition partner coverage.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The transposition partner coverage step uses rest[1:] instead of rest.

VERIFIED REPAIR

Use rest at the transposition partner coverage step.

Unsuccessful approach: The partial repair rest[:-1] still violates the transposition partner coverage invariant.

Case contract

Input 0<=n<=7; return lexicographically sorted permutations p of 0..n-1 satisfying p[p[i]]=i.

Why this case matters

Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x;out=[]
    def visit(p,free):
     if not free:
      out.append(p);return
     i=free[0]
     rest=[v for v in free if v!=i]
     q=p[:];q[i]=i
     visit(q,rest)
     for j in rest[1:]:
      q=p[:];q[i]=j;q[j]=i
      visit(q,[v for v in rest if v!=j])
    visit([-1]*n,list(range(n)))
    return sorted(out)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(2, [[0, 1], [1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (1, [[0]]), (3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]])], [(3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 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5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
explicit oracle 0	`[[0, 1]]`	`[[0, 1], [1, 0]]`	Failed
explicit oracle 1	`[[]]`	`[[]]`	Passed
explicit oracle 2	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 6, 4, 5, 3], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 5, 1, 4, 2, 6], [0, 3, 6, 1, 4, 5, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 5, 3, 1, 2, 6], [0, 4, 6, 3, 1, 5, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 4, 3, 2, 1, 6], [0, 5, 6, 3, 4, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 5, 3, 4, 2, 1], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 6, 4, 5, 3], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 5, 0, 4, 2, 6], [3, 1, 6, 0, 4, 5, 2], [3, 4, 2, 0, 1, 5, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 5, 3, 0, 2, 6], [4, 1, 6, 3, 0, 5, 2], [4, 3, 2, 1, 0, 5, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 4, 3, 2, 0, 6], [5, 1, 6, 3, 4, 0, 2], [5, 3, 2, 1, 4, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 5, 3, 4, 2, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]	Failed
explicit oracle 3	`[[0]]`	`[[0]]`	Passed
explicit oracle 4	`[[0, 1, 2], [2, 1, 0]]`	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	Failed
explicit oracle 5	`[[0, 1, 2, 3], [0, 3, 2, 1], [2, 1, 0, 3], [3, 1, 2, 0]]`	`[[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]`	Failed

SHA-256 / 2b25f55b4d5d948496c24cf31ddd28bad052a2ae4b51dafc7fe063caf5e7e40e

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x;out=[]
    def visit(p,free):
     if not free:
      out.append(p);return
     i=free[0]
     rest=[v for v in free if v!=i]
     q=p[:];q[i]=i
     visit(q,rest)
     for j in rest[:-1]:
      q=p[:];q[i]=j;q[j]=i
      visit(q,[v for v in rest if v!=j])
    visit([-1]*n,list(range(n)))
    return sorted(out)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(2, [[0, 1], [1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (1, [[0]]), (3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]])], [(3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 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2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
explicit oracle 0	`[[0, 1]]`	`[[0, 1], [1, 0]]`	Failed
explicit oracle 1	`[[]]`	`[[]]`	Passed
explicit oracle 2	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 5, 4, 3, 6], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 5, 4, 6], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 5, 2, 3, 6], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 4, 3, 2, 6], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 5, 4, 3, 6], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 5, 4, 6], [0, 3, 4, 1, 2, 5, 6], [0, 3, 5, 1, 4, 2, 6], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 5, 1, 3, 6], [0, 4, 3, 2, 1, 5, 6], [0, 4, 5, 3, 1, 2, 6], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 4, 3, 1, 6], [0, 5, 3, 2, 4, 1, 6], [0, 5, 4, 3, 2, 1, 6], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 5, 4, 3, 6], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 5, 4, 6], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 5, 2, 3, 6], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 4, 3, 2, 6], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 5, 4, 3, 6], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 5, 4, 6], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 5, 1, 3, 6], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 4, 3, 1, 6], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 5, 4, 6], [3, 1, 4, 0, 2, 5, 6], [3, 1, 5, 0, 4, 2, 6], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 5, 4, 6], [3, 4, 2, 0, 1, 5, 6], [3, 4, 5, 0, 1, 2, 6], [3, 5, 2, 0, 4, 1, 6], [3, 5, 4, 0, 2, 1, 6], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 5, 0, 3, 6], [4, 1, 3, 2, 0, 5, 6], [4, 1, 5, 3, 0, 2, 6], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 5, 0, 3, 6], [4, 3, 2, 1, 0, 5, 6], [4, 3, 5, 1, 0, 2, 6], [4, 5, 2, 3, 0, 1, 6], [4, 5, 3, 2, 0, 1, 6], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 4, 3, 0, 6], [5, 1, 3, 2, 4, 0, 6], [5, 1, 4, 3, 2, 0, 6], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 4, 3, 0, 6], [5, 3, 2, 1, 4, 0, 6], [5, 3, 4, 1, 2, 0, 6], [5, 4, 2, 3, 1, 0, 6], [5, 4, 3, 2, 1, 0, 6]]	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]	Failed
explicit oracle 3	`[[0]]`	`[[0]]`	Passed
explicit oracle 4	`[[0, 1, 2], [1, 0, 2]]`	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	Failed
explicit oracle 5	`[[0, 1, 2, 3], [0, 2, 1, 3], [1, 0, 2, 3], [2, 1, 0, 3]]`	`[[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]`	Failed

SHA-256 / f17d4ebee2d2bffaa7f6957d67c141506bb9f588a1fd6c67563b115a86f883e2

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n=x;out=[]
    def visit(p,free):
     if not free:
      out.append(p);return
     i=free[0]
     rest=[v for v in free if v!=i]
     q=p[:];q[i]=i
     visit(q,rest)
     for j in rest:
      q=p[:];q[i]=j;q[j]=i
      visit(q,[v for v in rest if v!=j])
    visit([-1]*n,list(range(n)))
    return sorted(out)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(2, [[0, 1], [1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (1, [[0]]), (3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]])], [(3, [[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]]), (0, [[]]), (7, [[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 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2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]), (4, [[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]), (5, [[0, 1, 2, 3, 4], [0, 1, 2, 4, 3], [0, 1, 3, 2, 4], [0, 1, 4, 3, 2], [0, 2, 1, 3, 4], [0, 2, 1, 4, 3], [0, 3, 2, 1, 4], [0, 3, 4, 1, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 2, 3, 4], [1, 0, 2, 4, 3], [1, 0, 3, 2, 4], [1, 0, 4, 3, 2], [2, 1, 0, 3, 4], [2, 1, 0, 4, 3], [2, 3, 0, 1, 4], [2, 4, 0, 3, 1], [3, 1, 2, 0, 4], [3, 1, 4, 0, 2], [3, 2, 1, 0, 4], [3, 4, 2, 0, 1], [4, 1, 2, 3, 0], [4, 1, 3, 2, 0], [4, 2, 1, 3, 0], [4, 3, 2, 1, 0]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
explicit oracle 0	`[[0, 1], [1, 0]]`	`[[0, 1], [1, 0]]`	Passed
explicit oracle 1	`[[]]`	`[[]]`	Passed
explicit oracle 2	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]	[[0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 6, 5], [0, 1, 2, 3, 5, 4, 6], [0, 1, 2, 3, 6, 5, 4], [0, 1, 2, 4, 3, 5, 6], [0, 1, 2, 4, 3, 6, 5], [0, 1, 2, 5, 4, 3, 6], [0, 1, 2, 5, 6, 3, 4], [0, 1, 2, 6, 4, 5, 3], [0, 1, 2, 6, 5, 4, 3], [0, 1, 3, 2, 4, 5, 6], [0, 1, 3, 2, 4, 6, 5], [0, 1, 3, 2, 5, 4, 6], [0, 1, 3, 2, 6, 5, 4], [0, 1, 4, 3, 2, 5, 6], [0, 1, 4, 3, 2, 6, 5], [0, 1, 4, 5, 2, 3, 6], [0, 1, 4, 6, 2, 5, 3], [0, 1, 5, 3, 4, 2, 6], [0, 1, 5, 3, 6, 2, 4], [0, 1, 5, 4, 3, 2, 6], [0, 1, 5, 6, 4, 2, 3], [0, 1, 6, 3, 4, 5, 2], [0, 1, 6, 3, 5, 4, 2], [0, 1, 6, 4, 3, 5, 2], [0, 1, 6, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5, 6], [0, 2, 1, 3, 4, 6, 5], [0, 2, 1, 3, 5, 4, 6], [0, 2, 1, 3, 6, 5, 4], [0, 2, 1, 4, 3, 5, 6], [0, 2, 1, 4, 3, 6, 5], [0, 2, 1, 5, 4, 3, 6], [0, 2, 1, 5, 6, 3, 4], [0, 2, 1, 6, 4, 5, 3], [0, 2, 1, 6, 5, 4, 3], [0, 3, 2, 1, 4, 5, 6], [0, 3, 2, 1, 4, 6, 5], [0, 3, 2, 1, 5, 4, 6], [0, 3, 2, 1, 6, 5, 4], [0, 3, 4, 1, 2, 5, 6], [0, 3, 4, 1, 2, 6, 5], [0, 3, 5, 1, 4, 2, 6], [0, 3, 5, 1, 6, 2, 4], [0, 3, 6, 1, 4, 5, 2], [0, 3, 6, 1, 5, 4, 2], [0, 4, 2, 3, 1, 5, 6], [0, 4, 2, 3, 1, 6, 5], [0, 4, 2, 5, 1, 3, 6], [0, 4, 2, 6, 1, 5, 3], [0, 4, 3, 2, 1, 5, 6], [0, 4, 3, 2, 1, 6, 5], [0, 4, 5, 3, 1, 2, 6], [0, 4, 5, 6, 1, 2, 3], [0, 4, 6, 3, 1, 5, 2], [0, 4, 6, 5, 1, 3, 2], [0, 5, 2, 3, 4, 1, 6], [0, 5, 2, 3, 6, 1, 4], [0, 5, 2, 4, 3, 1, 6], [0, 5, 2, 6, 4, 1, 3], [0, 5, 3, 2, 4, 1, 6], [0, 5, 3, 2, 6, 1, 4], [0, 5, 4, 3, 2, 1, 6], [0, 5, 4, 6, 2, 1, 3], [0, 5, 6, 3, 4, 1, 2], [0, 5, 6, 4, 3, 1, 2], [0, 6, 2, 3, 4, 5, 1], [0, 6, 2, 3, 5, 4, 1], [0, 6, 2, 4, 3, 5, 1], [0, 6, 2, 5, 4, 3, 1], [0, 6, 3, 2, 4, 5, 1], [0, 6, 3, 2, 5, 4, 1], [0, 6, 4, 3, 2, 5, 1], [0, 6, 4, 5, 2, 3, 1], [0, 6, 5, 3, 4, 2, 1], [0, 6, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5, 6], [1, 0, 2, 3, 4, 6, 5], [1, 0, 2, 3, 5, 4, 6], [1, 0, 2, 3, 6, 5, 4], [1, 0, 2, 4, 3, 5, 6], [1, 0, 2, 4, 3, 6, 5], [1, 0, 2, 5, 4, 3, 6], [1, 0, 2, 5, 6, 3, 4], [1, 0, 2, 6, 4, 5, 3], [1, 0, 2, 6, 5, 4, 3], [1, 0, 3, 2, 4, 5, 6], [1, 0, 3, 2, 4, 6, 5], [1, 0, 3, 2, 5, 4, 6], [1, 0, 3, 2, 6, 5, 4], [1, 0, 4, 3, 2, 5, 6], [1, 0, 4, 3, 2, 6, 5], [1, 0, 4, 5, 2, 3, 6], [1, 0, 4, 6, 2, 5, 3], [1, 0, 5, 3, 4, 2, 6], [1, 0, 5, 3, 6, 2, 4], [1, 0, 5, 4, 3, 2, 6], [1, 0, 5, 6, 4, 2, 3], [1, 0, 6, 3, 4, 5, 2], [1, 0, 6, 3, 5, 4, 2], [1, 0, 6, 4, 3, 5, 2], [1, 0, 6, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5, 6], [2, 1, 0, 3, 4, 6, 5], [2, 1, 0, 3, 5, 4, 6], [2, 1, 0, 3, 6, 5, 4], [2, 1, 0, 4, 3, 5, 6], [2, 1, 0, 4, 3, 6, 5], [2, 1, 0, 5, 4, 3, 6], [2, 1, 0, 5, 6, 3, 4], [2, 1, 0, 6, 4, 5, 3], [2, 1, 0, 6, 5, 4, 3], [2, 3, 0, 1, 4, 5, 6], [2, 3, 0, 1, 4, 6, 5], [2, 3, 0, 1, 5, 4, 6], [2, 3, 0, 1, 6, 5, 4], [2, 4, 0, 3, 1, 5, 6], [2, 4, 0, 3, 1, 6, 5], [2, 4, 0, 5, 1, 3, 6], [2, 4, 0, 6, 1, 5, 3], [2, 5, 0, 3, 4, 1, 6], [2, 5, 0, 3, 6, 1, 4], [2, 5, 0, 4, 3, 1, 6], [2, 5, 0, 6, 4, 1, 3], [2, 6, 0, 3, 4, 5, 1], [2, 6, 0, 3, 5, 4, 1], [2, 6, 0, 4, 3, 5, 1], [2, 6, 0, 5, 4, 3, 1], [3, 1, 2, 0, 4, 5, 6], [3, 1, 2, 0, 4, 6, 5], [3, 1, 2, 0, 5, 4, 6], [3, 1, 2, 0, 6, 5, 4], [3, 1, 4, 0, 2, 5, 6], [3, 1, 4, 0, 2, 6, 5], [3, 1, 5, 0, 4, 2, 6], [3, 1, 5, 0, 6, 2, 4], [3, 1, 6, 0, 4, 5, 2], [3, 1, 6, 0, 5, 4, 2], [3, 2, 1, 0, 4, 5, 6], [3, 2, 1, 0, 4, 6, 5], [3, 2, 1, 0, 5, 4, 6], [3, 2, 1, 0, 6, 5, 4], [3, 4, 2, 0, 1, 5, 6], [3, 4, 2, 0, 1, 6, 5], [3, 4, 5, 0, 1, 2, 6], [3, 4, 6, 0, 1, 5, 2], [3, 5, 2, 0, 4, 1, 6], [3, 5, 2, 0, 6, 1, 4], [3, 5, 4, 0, 2, 1, 6], [3, 5, 6, 0, 4, 1, 2], [3, 6, 2, 0, 4, 5, 1], [3, 6, 2, 0, 5, 4, 1], [3, 6, 4, 0, 2, 5, 1], [3, 6, 5, 0, 4, 2, 1], [4, 1, 2, 3, 0, 5, 6], [4, 1, 2, 3, 0, 6, 5], [4, 1, 2, 5, 0, 3, 6], [4, 1, 2, 6, 0, 5, 3], [4, 1, 3, 2, 0, 5, 6], [4, 1, 3, 2, 0, 6, 5], [4, 1, 5, 3, 0, 2, 6], [4, 1, 5, 6, 0, 2, 3], [4, 1, 6, 3, 0, 5, 2], [4, 1, 6, 5, 0, 3, 2], [4, 2, 1, 3, 0, 5, 6], [4, 2, 1, 3, 0, 6, 5], [4, 2, 1, 5, 0, 3, 6], [4, 2, 1, 6, 0, 5, 3], [4, 3, 2, 1, 0, 5, 6], [4, 3, 2, 1, 0, 6, 5], [4, 3, 5, 1, 0, 2, 6], [4, 3, 6, 1, 0, 5, 2], [4, 5, 2, 3, 0, 1, 6], [4, 5, 2, 6, 0, 1, 3], [4, 5, 3, 2, 0, 1, 6], [4, 5, 6, 3, 0, 1, 2], [4, 6, 2, 3, 0, 5, 1], [4, 6, 2, 5, 0, 3, 1], [4, 6, 3, 2, 0, 5, 1], [4, 6, 5, 3, 0, 2, 1], [5, 1, 2, 3, 4, 0, 6], [5, 1, 2, 3, 6, 0, 4], [5, 1, 2, 4, 3, 0, 6], [5, 1, 2, 6, 4, 0, 3], [5, 1, 3, 2, 4, 0, 6], [5, 1, 3, 2, 6, 0, 4], [5, 1, 4, 3, 2, 0, 6], [5, 1, 4, 6, 2, 0, 3], [5, 1, 6, 3, 4, 0, 2], [5, 1, 6, 4, 3, 0, 2], [5, 2, 1, 3, 4, 0, 6], [5, 2, 1, 3, 6, 0, 4], [5, 2, 1, 4, 3, 0, 6], [5, 2, 1, 6, 4, 0, 3], [5, 3, 2, 1, 4, 0, 6], [5, 3, 2, 1, 6, 0, 4], [5, 3, 4, 1, 2, 0, 6], [5, 3, 6, 1, 4, 0, 2], [5, 4, 2, 3, 1, 0, 6], [5, 4, 2, 6, 1, 0, 3], [5, 4, 3, 2, 1, 0, 6], [5, 4, 6, 3, 1, 0, 2], [5, 6, 2, 3, 4, 0, 1], [5, 6, 2, 4, 3, 0, 1], [5, 6, 3, 2, 4, 0, 1], [5, 6, 4, 3, 2, 0, 1], [6, 1, 2, 3, 4, 5, 0], [6, 1, 2, 3, 5, 4, 0], [6, 1, 2, 4, 3, 5, 0], [6, 1, 2, 5, 4, 3, 0], [6, 1, 3, 2, 4, 5, 0], [6, 1, 3, 2, 5, 4, 0], [6, 1, 4, 3, 2, 5, 0], [6, 1, 4, 5, 2, 3, 0], [6, 1, 5, 3, 4, 2, 0], [6, 1, 5, 4, 3, 2, 0], [6, 2, 1, 3, 4, 5, 0], [6, 2, 1, 3, 5, 4, 0], [6, 2, 1, 4, 3, 5, 0], [6, 2, 1, 5, 4, 3, 0], [6, 3, 2, 1, 4, 5, 0], [6, 3, 2, 1, 5, 4, 0], [6, 3, 4, 1, 2, 5, 0], [6, 3, 5, 1, 4, 2, 0], [6, 4, 2, 3, 1, 5, 0], [6, 4, 2, 5, 1, 3, 0], [6, 4, 3, 2, 1, 5, 0], [6, 4, 5, 3, 1, 2, 0], [6, 5, 2, 3, 4, 1, 0], [6, 5, 2, 4, 3, 1, 0], [6, 5, 3, 2, 4, 1, 0], [6, 5, 4, 3, 2, 1, 0]]	Passed
explicit oracle 3	`[[0]]`	`[[0]]`	Passed
explicit oracle 4	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	Passed
explicit oracle 5	`[[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]`	`[[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 3, 2, 1], [1, 0, 2, 3], [1, 0, 3, 2], [2, 1, 0, 3], [2, 3, 0, 1], [3, 1, 2, 0], [3, 2, 1, 0]]`	Passed

SHA-256 / 8376c10e4d4d51c0dc3fdcbdb9625765e87d691e8b2b0eeb1b6c9ddc98a2a1f5

Verification & scope

A deterministic bounded teaching model. Inputs are restricted to the explicit contract; this is not a production algebra library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:39:25.505175+00:00.

Case digest / f968d03a0832ed8361d392ca871432c893eb2fa73fdb2ee1b0605887a28aece4