FA-15331 / Numerics / Open access

Involution permutations: transposition first image · case 01

The exact involution permutations result violates the stated contract at transposition first image.

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

ROOT CAUSE

The transposition first image step uses i instead of j.

VERIFIED REPAIR

Use j at the transposition first image step.

Unsuccessful approach: The partial repair p[j] still violates the transposition first image 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:
      q=p[:];q[i]=i;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, 0], [0, 1]]`	`[[0, 1], [1, 0]]`	Failed
explicit oracle 1	`[[]]`	`[[]]`	Passed
explicit oracle 2	[[0, 0, 2, 2, 4, 4, 6], [0, 0, 2, 2, 4, 5, 4], [0, 0, 2, 2, 4, 5, 5], [0, 0, 2, 2, 4, 5, 6], [0, 0, 2, 3, 2, 3, 6], [0, 0, 2, 3, 2, 5, 3], [0, 0, 2, 3, 2, 5, 5], [0, 0, 2, 3, 2, 5, 6], [0, 0, 2, 3, 3, 2, 6], [0, 0, 2, 3, 3, 5, 2], [0, 0, 2, 3, 3, 5, 5], [0, 0, 2, 3, 3, 5, 6], [0, 0, 2, 3, 4, 2, 3], [0, 0, 2, 3, 4, 2, 4], [0, 0, 2, 3, 4, 2, 6], [0, 0, 2, 3, 4, 3, 2], [0, 0, 2, 3, 4, 3, 4], [0, 0, 2, 3, 4, 3, 6], [0, 0, 2, 3, 4, 4, 2], [0, 0, 2, 3, 4, 4, 3], [0, 0, 2, 3, 4, 4, 6], [0, 0, 2, 3, 4, 5, 2], [0, 0, 2, 3, 4, 5, 3], [0, 0, 2, 3, 4, 5, 4], [0, 0, 2, 3, 4, 5, 5], [0, 0, 2, 3, 4, 5, 6], [0, 1, 0, 1, 4, 4, 6], [0, 1, 0, 1, 4, 5, 4], [0, 1, 0, 1, 4, 5, 5], [0, 1, 0, 1, 4, 5, 6], [0, 1, 0, 3, 1, 3, 6], [0, 1, 0, 3, 1, 5, 3], [0, 1, 0, 3, 1, 5, 5], [0, 1, 0, 3, 1, 5, 6], [0, 1, 0, 3, 3, 1, 6], [0, 1, 0, 3, 3, 5, 1], [0, 1, 0, 3, 3, 5, 5], [0, 1, 0, 3, 3, 5, 6], [0, 1, 0, 3, 4, 1, 3], [0, 1, 0, 3, 4, 1, 4], [0, 1, 0, 3, 4, 1, 6], [0, 1, 0, 3, 4, 3, 1], [0, 1, 0, 3, 4, 3, 4], [0, 1, 0, 3, 4, 3, 6], [0, 1, 0, 3, 4, 4, 1], [0, 1, 0, 3, 4, 4, 3], [0, 1, 0, 3, 4, 4, 6], [0, 1, 0, 3, 4, 5, 1], [0, 1, 0, 3, 4, 5, 3], [0, 1, 0, 3, 4, 5, 4], [0, 1, 0, 3, 4, 5, 5], [0, 1, 0, 3, 4, 5, 6], [0, 1, 1, 0, 4, 4, 6], [0, 1, 1, 0, 4, 5, 4], [0, 1, 1, 0, 4, 5, 5], [0, 1, 1, 0, 4, 5, 6], [0, 1, 1, 3, 0, 3, 6], [0, 1, 1, 3, 0, 5, 3], [0, 1, 1, 3, 0, 5, 5], [0, 1, 1, 3, 0, 5, 6], [0, 1, 1, 3, 3, 0, 6], [0, 1, 1, 3, 3, 5, 0], [0, 1, 1, 3, 3, 5, 5], [0, 1, 1, 3, 3, 5, 6], [0, 1, 1, 3, 4, 0, 3], [0, 1, 1, 3, 4, 0, 4], [0, 1, 1, 3, 4, 0, 6], [0, 1, 1, 3, 4, 3, 0], [0, 1, 1, 3, 4, 3, 4], [0, 1, 1, 3, 4, 3, 6], [0, 1, 1, 3, 4, 4, 0], [0, 1, 1, 3, 4, 4, 3], [0, 1, 1, 3, 4, 4, 6], [0, 1, 1, 3, 4, 5, 0], [0, 1, 1, 3, 4, 5, 3], [0, 1, 1, 3, 4, 5, 4], [0, 1, 1, 3, 4, 5, 5], [0, 1, 1, 3, 4, 5, 6], [0, 1, 2, 0, 1, 2, 6], [0, 1, 2, 0, 1, 5, 2], [0, 1, 2, 0, 1, 5, 5], [0, 1, 2, 0, 1, 5, 6], [0, 1, 2, 0, 2, 1, 6], [0, 1, 2, 0, 2, 5, 1], [0, 1, 2, 0, 2, 5, 5], [0, 1, 2, 0, 2, 5, 6], [0, 1, 2, 0, 4, 1, 2], [0, 1, 2, 0, 4, 1, 4], [0, 1, 2, 0, 4, 1, 6], [0, 1, 2, 0, 4, 2, 1], [0, 1, 2, 0, 4, 2, 4], [0, 1, 2, 0, 4, 2, 6], [0, 1, 2, 0, 4, 4, 1], [0, 1, 2, 0, 4, 4, 2], [0, 1, 2, 0, 4, 4, 6], [0, 1, 2, 0, 4, 5, 1], [0, 1, 2, 0, 4, 5, 2], [0, 1, 2, 0, 4, 5, 4], [0, 1, 2, 0, 4, 5, 5], [0, 1, 2, 0, 4, 5, 6], [0, 1, 2, 1, 0, 2, 6], [0, 1, 2, 1, 0, 5, 2], [0, 1, 2, 1, 0, 5, 5], [0, 1, 2, 1, 0, 5, 6], [0, 1, 2, 1, 2, 0, 6], [0, 1, 2, 1, 2, 5, 0], [0, 1, 2, 1, 2, 5, 5], [0, 1, 2, 1, 2, 5, 6], [0, 1, 2, 1, 4, 0, 2], [0, 1, 2, 1, 4, 0, 4], [0, 1, 2, 1, 4, 0, 6], [0, 1, 2, 1, 4, 2, 0], [0, 1, 2, 1, 4, 2, 4], [0, 1, 2, 1, 4, 2, 6], [0, 1, 2, 1, 4, 4, 0], [0, 1, 2, 1, 4, 4, 2], [0, 1, 2, 1, 4, 4, 6], [0, 1, 2, 1, 4, 5, 0], [0, 1, 2, 1, 4, 5, 2], [0, 1, 2, 1, 4, 5, 4], [0, 1, 2, 1, 4, 5, 5], [0, 1, 2, 1, 4, 5, 6], [0, 1, 2, 2, 0, 1, 6], [0, 1, 2, 2, 0, 5, 1], [0, 1, 2, 2, 0, 5, 5], [0, 1, 2, 2, 0, 5, 6], [0, 1, 2, 2, 1, 0, 6], [0, 1, 2, 2, 1, 5, 0], [0, 1, 2, 2, 1, 5, 5], [0, 1, 2, 2, 1, 5, 6], [0, 1, 2, 2, 4, 0, 1], [0, 1, 2, 2, 4, 0, 4], [0, 1, 2, 2, 4, 0, 6], [0, 1, 2, 2, 4, 1, 0], [0, 1, 2, 2, 4, 1, 4], [0, 1, 2, 2, 4, 1, 6], [0, 1, 2, 2, 4, 4, 0], [0, 1, 2, 2, 4, 4, 1], [0, 1, 2, 2, 4, 4, 6], [0, 1, 2, 2, 4, 5, 0], [0, 1, 2, 2, 4, 5, 1], [0, 1, 2, 2, 4, 5, 4], [0, 1, 2, 2, 4, 5, 5], [0, 1, 2, 2, 4, 5, 6], [0, 1, 2, 3, 0, 1, 2], [0, 1, 2, 3, 0, 1, 3], [0, 1, 2, 3, 0, 1, 6], [0, 1, 2, 3, 0, 2, 1], [0, 1, 2, 3, 0, 2, 3], [0, 1, 2, 3, 0, 2, 6], [0, 1, 2, 3, 0, 3, 1], [0, 1, 2, 3, 0, 3, 2], [0, 1, 2, 3, 0, 3, 6], [0, 1, 2, 3, 0, 5, 1], [0, 1, 2, 3, 0, 5, 2], [0, 1, 2, 3, 0, 5, 3], [0, 1, 2, 3, 0, 5, 5], [0, 1, 2, 3, 0, 5, 6], [0, 1, 2, 3, 1, 0, 2], [0, 1, 2, 3, 1, 0, 3], [0, 1, 2, 3, 1, 0, 6], [0, 1, 2, 3, 1, 2, 0], [0, 1, 2, 3, 1, 2, 3], [0, 1, 2, 3, 1, 2, 6], [0, 1, 2, 3, 1, 3, 0], [0, 1, 2, 3, 1, 3, 2], [0, 1, 2, 3, 1, 3, 6], [0, 1, 2, 3, 1, 5, 0], [0, 1, 2, 3, 1, 5, 2], [0, 1, 2, 3, 1, 5, 3], [0, 1, 2, 3, 1, 5, 5], [0, 1, 2, 3, 1, 5, 6], [0, 1, 2, 3, 2, 0, 1], [0, 1, 2, 3, 2, 0, 3], [0, 1, 2, 3, 2, 0, 6], [0, 1, 2, 3, 2, 1, 0], [0, 1, 2, 3, 2, 1, 3], [0, 1, 2, 3, 2, 1, 6], [0, 1, 2, 3, 2, 3, 0], [0, 1, 2, 3, 2, 3, 1], [0, 1, 2, 3, 2, 3, 6], [0, 1, 2, 3, 2, 5, 0], [0, 1, 2, 3, 2, 5, 1], [0, 1, 2, 3, 2, 5, 3], [0, 1, 2, 3, 2, 5, 5], [0, 1, 2, 3, 2, 5, 6], [0, 1, 2, 3, 3, 0, 1], [0, 1, 2, 3, 3, 0, 2], [0, 1, 2, 3, 3, 0, 6], [0, 1, 2, 3, 3, 1, 0], [0, 1, 2, 3, 3, 1, 2], [0, 1, 2, 3, 3, 1, 6], [0, 1, 2, 3, 3, 2, 0], [0, 1, 2, 3, 3, 2, 1], [0, 1, 2, 3, 3, 2, 6], [0, 1, 2, 3, 3, 5, 0], [0, 1, 2, 3, 3, 5, 1], [0, 1, 2, 3, 3, 5, 2], [0, 1, 2, 3, 3, 5, 5], [0, 1, 2, 3, 3, 5, 6], [0, 1, 2, 3, 4, 0, 1], [0, 1, 2, 3, 4, 0, 2], [0, 1, 2, 3, 4, 0, 3], [0, 1, 2, 3, 4, 0, 4], [0, 1, 2, 3, 4, 0, 6], [0, 1, 2, 3, 4, 1, 0], [0, 1, 2, 3, 4, 1, 2], [0, 1, 2, 3, 4, 1, 3], [0, 1, 2, 3, 4, 1, 4], [0, 1, 2, 3, 4, 1, 6], [0, 1, 2, 3, 4, 2, 0], [0, 1, 2, 3, 4, 2, 1], [0, 1, 2, 3, 4, 2, 3], [0, 1, 2, 3, 4, 2, 4], [0, 1, 2, 3, 4, 2, 6], [0, 1, 2, 3, 4, 3, 0], [0, 1, 2, 3, 4, 3, 1], [0, 1, 2, 3, 4, 3, 2], [0, 1, 2, 3, 4, 3, 4], [0, 1, 2, 3, 4, 3, 6], [0, 1, 2, 3, 4, 4, 0], [0, 1, 2, 3, 4, 4, 1], [0, 1, 2, 3, 4, 4, 2], [0, 1, 2, 3, 4, 4, 3], [0, 1, 2, 3, 4, 4, 6], [0, 1, 2, 3, 4, 5, 0], [0, 1, 2, 3, 4, 5, 1], [0, 1, 2, 3, 4, 5, 2], [0, 1, 2, 3, 4, 5, 3], [0, 1, 2, 3, 4, 5, 4], [0, 1, 2, 3, 4, 5, 5], [0, 1, 2, 3, 4, 5, 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, 0, 2], [0, 1, 0], [0, 1, 1], [0, 1, 2]]`	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	Failed
explicit oracle 5	`[[0, 0, 2, 2], [0, 0, 2, 3], [0, 1, 0, 1], [0, 1, 0, 3], [0, 1, 1, 0], [0, 1, 1, 3], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2], [0, 1, 2, 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 / e5a6b999e96ab73fea5df073a709f949a1ebfb22dc309f82e7f84cae43e0a3dd

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:
      q=p[:];q[i]=p[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, 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1], [0, 5, 3, 2, 4, 1], [0, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5], [1, 0, 2, 3, 5, 4], [1, 0, 2, 4, 3, 5], [1, 0, 2, 5, 4, 3], [1, 0, 3, 2, 4, 5], [1, 0, 3, 2, 5, 4], [1, 0, 4, 3, 2, 5], [1, 0, 4, 5, 2, 3], [1, 0, 5, 3, 4, 2], [1, 0, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5], [2, 1, 0, 3, 5, 4], [2, 1, 0, 4, 3, 5], [2, 1, 0, 5, 4, 3], [2, 3, 0, 1, 4, 5], [2, 3, 0, 1, 5, 4], [2, 4, 0, 3, 1, 5], [2, 4, 0, 5, 1, 3], [2, 5, 0, 3, 4, 1], [2, 5, 0, 4, 3, 1], [3, 1, 2, 0, 4, 5], [3, 1, 2, 0, 5, 4], [3, 1, 4, 0, 2, 5], [3, 1, 5, 0, 4, 2], [3, 2, 1, 0, 4, 5], [3, 2, 1, 0, 5, 4], [3, 4, 2, 0, 1, 5], [3, 4, 5, 0, 1, 2], [3, 5, 2, 0, 4, 1], [3, 5, 4, 0, 2, 1], [4, 1, 2, 3, 0, 5], [4, 1, 2, 5, 0, 3], [4, 1, 3, 2, 0, 5], [4, 1, 5, 3, 0, 2], [4, 2, 1, 3, 0, 5], [4, 2, 1, 5, 0, 3], [4, 3, 2, 1, 0, 5], [4, 3, 5, 1, 0, 2], [4, 5, 2, 3, 0, 1], [4, 5, 3, 2, 0, 1], [5, 1, 2, 3, 4, 0], [5, 1, 2, 4, 3, 0], [5, 1, 3, 2, 4, 0], [5, 1, 4, 3, 2, 0], [5, 2, 1, 3, 4, 0], [5, 2, 1, 4, 3, 0], [5, 3, 2, 1, 4, 0], [5, 3, 4, 1, 2, 0], [5, 4, 2, 3, 1, 0], [5, 4, 3, 2, 1, 0]])], [(6, [[0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5, 4], [0, 1, 2, 4, 3, 5], [0, 1, 2, 5, 4, 3], [0, 1, 3, 2, 4, 5], [0, 1, 3, 2, 5, 4], [0, 1, 4, 3, 2, 5], [0, 1, 4, 5, 2, 3], [0, 1, 5, 3, 4, 2], [0, 1, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5], [0, 2, 1, 3, 5, 4], [0, 2, 1, 4, 3, 5], [0, 2, 1, 5, 4, 3], [0, 3, 2, 1, 4, 5], [0, 3, 2, 1, 5, 4], [0, 3, 4, 1, 2, 5], [0, 3, 5, 1, 4, 2], [0, 4, 2, 3, 1, 5], [0, 4, 2, 5, 1, 3], [0, 4, 3, 2, 1, 5], [0, 4, 5, 3, 1, 2], [0, 5, 2, 3, 4, 1], [0, 5, 2, 4, 3, 1], [0, 5, 3, 2, 4, 1], [0, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5], [1, 0, 2, 3, 5, 4], [1, 0, 2, 4, 3, 5], [1, 0, 2, 5, 4, 3], [1, 0, 3, 2, 4, 5], [1, 0, 3, 2, 5, 4], [1, 0, 4, 3, 2, 5], [1, 0, 4, 5, 2, 3], [1, 0, 5, 3, 4, 2], [1, 0, 5, 4, 3, 2], [2, 1, 0, 3, 4, 5], [2, 1, 0, 3, 5, 4], [2, 1, 0, 4, 3, 5], [2, 1, 0, 5, 4, 3], [2, 3, 0, 1, 4, 5], [2, 3, 0, 1, 5, 4], [2, 4, 0, 3, 1, 5], [2, 4, 0, 5, 1, 3], [2, 5, 0, 3, 4, 1], [2, 5, 0, 4, 3, 1], [3, 1, 2, 0, 4, 5], [3, 1, 2, 0, 5, 4], [3, 1, 4, 0, 2, 5], [3, 1, 5, 0, 4, 2], [3, 2, 1, 0, 4, 5], [3, 2, 1, 0, 5, 4], [3, 4, 2, 0, 1, 5], [3, 4, 5, 0, 1, 2], [3, 5, 2, 0, 4, 1], [3, 5, 4, 0, 2, 1], [4, 1, 2, 3, 0, 5], [4, 1, 2, 5, 0, 3], [4, 1, 3, 2, 0, 5], [4, 1, 5, 3, 0, 2], [4, 2, 1, 3, 0, 5], [4, 2, 1, 5, 0, 3], [4, 3, 2, 1, 0, 5], [4, 3, 5, 1, 0, 2], [4, 5, 2, 3, 0, 1], [4, 5, 3, 2, 0, 1], [5, 1, 2, 3, 4, 0], [5, 1, 2, 4, 3, 0], [5, 1, 3, 2, 4, 0], [5, 1, 4, 3, 2, 0], [5, 2, 1, 3, 4, 0], [5, 2, 1, 4, 3, 0], [5, 3, 2, 1, 4, 0], [5, 3, 4, 1, 2, 0], [5, 4, 2, 3, 1, 0], [5, 4, 3, 2, 1, 0]]), (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]]), (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	`[[-1, 0], [0, 1]]`	`[[0, 1], [1, 0]]`	Failed
explicit oracle 1	`[[]]`	`[[]]`	Passed
explicit oracle 2	[[-1, -1, -1, 0, 1, 2, 6], [-1, -1, -1, 0, 1, 5, 2], [-1, -1, -1, 0, 2, 1, 6], [-1, -1, -1, 0, 2, 5, 1], [-1, -1, -1, 0, 4, 1, 2], [-1, -1, -1, 0, 4, 2, 1], [-1, -1, -1, 1, 0, 2, 6], [-1, -1, -1, 1, 0, 5, 2], [-1, -1, -1, 1, 2, 0, 6], [-1, -1, -1, 1, 2, 5, 0], [-1, -1, -1, 1, 4, 0, 2], [-1, -1, -1, 1, 4, 2, 0], [-1, -1, -1, 2, 0, 1, 6], [-1, -1, -1, 2, 0, 5, 1], [-1, -1, -1, 2, 1, 0, 6], [-1, -1, -1, 2, 1, 5, 0], [-1, -1, -1, 2, 4, 0, 1], [-1, -1, -1, 2, 4, 1, 0], [-1, -1, -1, 3, 0, 1, 2], [-1, -1, -1, 3, 0, 2, 1], [-1, -1, -1, 3, 1, 0, 2], [-1, -1, -1, 3, 1, 2, 0], [-1, -1, -1, 3, 2, 0, 1], [-1, -1, -1, 3, 2, 1, 0], [-1, -1, 0, -1, 1, 3, 6], [-1, -1, 0, -1, 1, 5, 3], [-1, -1, 0, -1, 3, 1, 6], [-1, -1, 0, -1, 3, 5, 1], [-1, -1, 0, -1, 4, 1, 3], [-1, -1, 0, -1, 4, 3, 1], [-1, -1, 0, 1, -1, 4, 6], [-1, -1, 0, 1, -1, 5, 4], [-1, -1, 0, 1, 4, -1, 5], [-1, -1, 0, 1, 4, 5, 6], [-1, -1, 0, 3, -1, 1, 4], [-1, -1, 0, 3, -1, 4, 1], [-1, -1, 0, 3, 1, -1, 5], [-1, -1, 0, 3, 1, 5, 6], [-1, -1, 0, 3, 4, 1, 6], [-1, -1, 0, 3, 4, 5, 1], [-1, -1, 1, -1, 0, 3, 6], [-1, -1, 1, -1, 0, 5, 3], [-1, -1, 1, -1, 3, 0, 6], [-1, -1, 1, -1, 3, 5, 0], [-1, -1, 1, -1, 4, 0, 3], [-1, -1, 1, -1, 4, 3, 0], [-1, -1, 1, 0, -1, 4, 6], [-1, -1, 1, 0, -1, 5, 4], [-1, -1, 1, 0, 4, -1, 5], [-1, -1, 1, 0, 4, 5, 6], [-1, -1, 1, 3, -1, 0, 4], [-1, -1, 1, 3, -1, 4, 0], [-1, -1, 1, 3, 0, -1, 5], [-1, -1, 1, 3, 0, 5, 6], [-1, -1, 1, 3, 4, 0, 6], [-1, -1, 1, 3, 4, 5, 0], [-1, -1, 2, -1, 0, 1, 3], [-1, -1, 2, -1, 0, 3, 1], [-1, -1, 2, -1, 1, 0, 3], [-1, -1, 2, -1, 1, 3, 0], [-1, -1, 2, -1, 3, 0, 1], [-1, -1, 2, -1, 3, 1, 0], [-1, -1, 2, 0, -1, 1, 4], [-1, -1, 2, 0, -1, 4, 1], [-1, -1, 2, 0, 1, -1, 5], [-1, -1, 2, 0, 1, 5, 6], [-1, -1, 2, 0, 4, 1, 6], [-1, -1, 2, 0, 4, 5, 1], [-1, -1, 2, 1, -1, 0, 4], [-1, -1, 2, 1, -1, 4, 0], [-1, -1, 2, 1, 0, -1, 5], [-1, -1, 2, 1, 0, 5, 6], [-1, -1, 2, 1, 4, 0, 6], [-1, -1, 2, 1, 4, 5, 0], [-1, -1, 2, 3, 0, 1, 6], [-1, -1, 2, 3, 0, 5, 1], [-1, -1, 2, 3, 1, 0, 6], [-1, -1, 2, 3, 1, 5, 0], [-1, -1, 2, 3, 4, 0, 1], [-1, -1, 2, 3, 4, 1, 0], [-1, 0, -1, -1, 2, 3, 6], [-1, 0, -1, -1, 2, 5, 3], [-1, 0, -1, -1, 3, 2, 6], [-1, 0, -1, -1, 3, 5, 2], [-1, 0, -1, -1, 4, 2, 3], [-1, 0, -1, -1, 4, 3, 2], [-1, 0, -1, 2, -1, 4, 6], [-1, 0, -1, 2, -1, 5, 4], [-1, 0, -1, 2, 4, -1, 5], [-1, 0, -1, 2, 4, 5, 6], [-1, 0, -1, 3, -1, 2, 4], [-1, 0, -1, 3, -1, 4, 2], [-1, 0, -1, 3, 2, -1, 5], [-1, 0, -1, 3, 2, 5, 6], [-1, 0, -1, 3, 4, 2, 6], [-1, 0, -1, 3, 4, 5, 2], [-1, 0, 2, -1, -1, 3, 4], [-1, 0, 2, -1, -1, 4, 3], [-1, 0, 2, -1, 3, -1, 5], [-1, 0, 2, -1, 3, 5, 6], [-1, 0, 2, -1, 4, 3, 6], [-1, 0, 2, -1, 4, 5, 3], [-1, 0, 2, 3, -1, 4, 6], [-1, 0, 2, 3, -1, 5, 4], [-1, 0, 2, 3, 4, -1, 5], [-1, 0, 2, 3, 4, 5, 6], [-1, 1, -1, -1, 0, 2, 3], [-1, 1, -1, -1, 0, 3, 2], [-1, 1, -1, -1, 2, 0, 3], [-1, 1, -1, -1, 2, 3, 0], [-1, 1, -1, -1, 3, 0, 2], [-1, 1, -1, -1, 3, 2, 0], [-1, 1, -1, 0, -1, 2, 4], [-1, 1, -1, 0, -1, 4, 2], [-1, 1, -1, 0, 2, -1, 5], [-1, 1, -1, 0, 2, 5, 6], [-1, 1, -1, 0, 4, 2, 6], [-1, 1, -1, 0, 4, 5, 2], [-1, 1, -1, 2, -1, 0, 4], [-1, 1, -1, 2, -1, 4, 0], [-1, 1, -1, 2, 0, -1, 5], [-1, 1, -1, 2, 0, 5, 6], [-1, 1, -1, 2, 4, 0, 6], [-1, 1, -1, 2, 4, 5, 0], [-1, 1, -1, 3, 0, 2, 6], [-1, 1, -1, 3, 0, 5, 2], [-1, 1, -1, 3, 2, 0, 6], [-1, 1, -1, 3, 2, 5, 0], [-1, 1, -1, 3, 4, 0, 2], [-1, 1, -1, 3, 4, 2, 0], [-1, 1, 0, -1, -1, 3, 4], [-1, 1, 0, -1, -1, 4, 3], [-1, 1, 0, -1, 3, -1, 5], [-1, 1, 0, -1, 3, 5, 6], [-1, 1, 0, -1, 4, 3, 6], [-1, 1, 0, -1, 4, 5, 3], [-1, 1, 0, 3, -1, 4, 6], [-1, 1, 0, 3, -1, 5, 4], [-1, 1, 0, 3, 4, -1, 5], [-1, 1, 0, 3, 4, 5, 6], [-1, 1, 2, -1, 0, 3, 6], [-1, 1, 2, -1, 0, 5, 3], [-1, 1, 2, -1, 3, 0, 6], [-1, 1, 2, -1, 3, 5, 0], [-1, 1, 2, -1, 4, 0, 3], [-1, 1, 2, -1, 4, 3, 0], [-1, 1, 2, 0, -1, 4, 6], [-1, 1, 2, 0, -1, 5, 4], [-1, 1, 2, 0, 4, -1, 5], [-1, 1, 2, 0, 4, 5, 6], [-1, 1, 2, 3, -1, 0, 4], [-1, 1, 2, 3, -1, 4, 0], [-1, 1, 2, 3, 0, -1, 5], [-1, 1, 2, 3, 0, 5, 6], [-1, 1, 2, 3, 4, 0, 6], [-1, 1, 2, 3, 4, 5, 0], [0, -1, -1, -1, 1, 2, 3], [0, -1, -1, -1, 1, 3, 2], [0, -1, -1, -1, 2, 1, 3], [0, -1, -1, -1, 2, 3, 1], [0, -1, -1, -1, 3, 1, 2], [0, -1, -1, -1, 3, 2, 1], [0, -1, -1, 1, -1, 2, 4], [0, -1, -1, 1, -1, 4, 2], [0, -1, -1, 1, 2, -1, 5], [0, -1, -1, 1, 2, 5, 6], [0, -1, -1, 1, 4, 2, 6], [0, -1, -1, 1, 4, 5, 2], [0, -1, -1, 2, -1, 1, 4], [0, -1, -1, 2, -1, 4, 1], [0, -1, -1, 2, 1, -1, 5], [0, -1, -1, 2, 1, 5, 6], [0, -1, -1, 2, 4, 1, 6], [0, -1, -1, 2, 4, 5, 1], [0, -1, -1, 3, 1, 2, 6], [0, -1, -1, 3, 1, 5, 2], [0, -1, -1, 3, 2, 1, 6], [0, -1, -1, 3, 2, 5, 1], [0, -1, -1, 3, 4, 1, 2], [0, -1, -1, 3, 4, 2, 1], [0, -1, 1, -1, -1, 3, 4], [0, -1, 1, -1, -1, 4, 3], [0, -1, 1, -1, 3, -1, 5], [0, -1, 1, -1, 3, 5, 6], [0, -1, 1, -1, 4, 3, 6], [0, -1, 1, -1, 4, 5, 3], [0, -1, 1, 3, -1, 4, 6], [0, -1, 1, 3, -1, 5, 4], [0, -1, 1, 3, 4, -1, 5], [0, -1, 1, 3, 4, 5, 6], [0, -1, 2, -1, 1, 3, 6], [0, -1, 2, -1, 1, 5, 3], [0, -1, 2, -1, 3, 1, 6], [0, -1, 2, -1, 3, 5, 1], [0, -1, 2, -1, 4, 1, 3], [0, -1, 2, -1, 4, 3, 1], [0, -1, 2, 1, -1, 4, 6], [0, -1, 2, 1, -1, 5, 4], [0, -1, 2, 1, 4, -1, 5], [0, -1, 2, 1, 4, 5, 6], [0, -1, 2, 3, -1, 1, 4], [0, -1, 2, 3, -1, 4, 1], [0, -1, 2, 3, 1, -1, 5], [0, -1, 2, 3, 1, 5, 6], [0, -1, 2, 3, 4, 1, 6], [0, -1, 2, 3, 4, 5, 1], [0, 1, -1, -1, 2, 3, 6], [0, 1, -1, -1, 2, 5, 3], [0, 1, -1, -1, 3, 2, 6], [0, 1, -1, -1, 3, 5, 2], [0, 1, -1, -1, 4, 2, 3], [0, 1, -1, -1, 4, 3, 2], [0, 1, -1, 2, -1, 4, 6], [0, 1, -1, 2, -1, 5, 4], [0, 1, -1, 2, 4, -1, 5], [0, 1, -1, 2, 4, 5, 6], [0, 1, -1, 3, -1, 2, 4], [0, 1, -1, 3, -1, 4, 2], [0, 1, -1, 3, 2, -1, 5], [0, 1, -1, 3, 2, 5, 6], [0, 1, -1, 3, 4, 2, 6], [0, 1, -1, 3, 4, 5, 2], [0, 1, 2, -1, -1, 3, 4], [0, 1, 2, -1, -1, 4, 3], [0, 1, 2, -1, 3, -1, 5], [0, 1, 2, -1, 3, 5, 6], [0, 1, 2, -1, 4, 3, 6], [0, 1, 2, -1, 4, 5, 3], [0, 1, 2, 3, -1, 4, 6], [0, 1, 2, 3, -1, 5, 4], [0, 1, 2, 3, 4, -1, 5], [0, 1, 2, 3, 4, 5, 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	`[[-1, 0, 2], [-1, 1, 0], [0, -1, 1], [0, 1, 2]]`	`[[0, 1, 2], [0, 2, 1], [1, 0, 2], [2, 1, 0]]`	Failed
explicit oracle 5	`[[-1, -1, 0, 1], [-1, -1, 1, 0], [-1, 0, -1, 2], [-1, 0, 2, 3], [-1, 1, 0, 3], [-1, 1, 2, 0], [0, -1, 1, 3], [0, -1, 2, 1], [0, 1, -1, 2], [0, 1, 2, 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 / a94eef5dad80a0610818b3f4009b261a6c54ab59952f8a30788fac039ac6e4d9

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 2026-09-29T14:39:25.694967+00:00.

Case digest / d13d4fe3fe36f6db3b355ce6baddff57b16474309587a1d7d7db598858c7311a