FAILURE MAP
← Case archive

FA-15271 / Numerics / Open access

Integer partition enumeration: positive part admission · case 01

The exact integer partition enumeration result violates the stated contract at positive part admission.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The positive part admission step uses part==1 instead of part<=0.

VERIFIED REPAIR

Use part<=0 at the positive part admission step.

Unsuccessful approach: The partial repair part==hi still violates the positive part admission invariant.

Case contract

Input [n,L], n>=0 and L>=1; return partitions of n in descending part order, reverse lexicographic, each part<=L.

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,L=x;out=[]
    def visit(rem,hi,prefix):
     if rem==0:
      out.append(prefix);return
     for part in range(min(rem,hi),0,-1):
      if part==1:continue
      visit(rem-part,part,prefix+[part])
    visit(n,L,[])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([0, 2], [[]]), ([0, 3], [[]]), ([0, 4], [[]]), ([0, 5], [[]]), ([0, 6], [[]])], [([1, 2], [[1]]), ([2, 3], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([2, 2], [[2], [1, 1]]), ([2, 4], [[2], [1, 1]]), ([2, 5], [[2], [1, 1]]), ([2, 6], [[2], [1, 1]])], [([1, 3], [[1]]), ([2, 6], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([4, 3], [[3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 4], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 5], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 6], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]])], [([1, 4], [[1]]), ([3, 1], [[1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([6, 4], [[4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 5], [[5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 6], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 7], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]])], [([1, 5], [[1]]), ([3, 4], [[3], [2, 1], [1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 5], [[5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 6], [[6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 7], [[7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 8], [[8], [7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]])]]
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 fixtureActualExpectedOutcome
explicit oracle 0[][[1]]Failed
explicit oracle 1[[]][[]]Passed
explicit oracle 2[[8, 7], [8, 5, 2], [8, 4, 3], [8, 3, 2, 2], [7, 6, 2], [7, 5, 3], [7, 4, 4], [7, 4, 2, 2], [7, 3, 3, 2], [7, 2, 2, 2, 2], [6, 6, 3], [6, 5, 4], [6, 5, 2, 2], [6, 4, 3, 2], [6, 3, 3, 3], [6, 3, 2, 2, 2], [5, 5, 5], [5, 5, 3, 2], [5, 4, 4, 2], [5, 4, 3, 3], [5, 4, 2, 2, 2], [5, 3, 3, 2, 2], [5, 2, 2, 2, 2, 2], [4, 4, 4, 3], [4, 4, 3, 2, 2], [4, 3, 3, 3, 2], [4, 3, 2, 2, 2, 2], [3, 3, 3, 3, 3], [3, 3, 3, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2]][[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]Failed
explicit oracle 3[[]][[]]Passed
explicit oracle 4[[]][[]]Passed
explicit oracle 5[[]][[]]Passed
explicit oracle 6[[]][[]]Passed
explicit oracle 7[[]][[]]Passed

SHA-256 / e3e715af4f393e6c91391f89d46194abf0559d8754bb4b44691579b5ec3fc685

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,L=x;out=[]
    def visit(rem,hi,prefix):
     if rem==0:
      out.append(prefix);return
     for part in range(min(rem,hi),0,-1):
      if part==hi:continue
      visit(rem-part,part,prefix+[part])
    visit(n,L,[])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([0, 2], [[]]), ([0, 3], [[]]), ([0, 4], [[]]), ([0, 5], [[]]), ([0, 6], [[]])], [([1, 2], [[1]]), ([2, 3], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([2, 2], [[2], [1, 1]]), ([2, 4], [[2], [1, 1]]), ([2, 5], [[2], [1, 1]]), ([2, 6], [[2], [1, 1]])], [([1, 3], [[1]]), ([2, 6], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([4, 3], [[3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 4], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 5], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 6], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]])], [([1, 4], [[1]]), ([3, 1], [[1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([6, 4], [[4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 5], [[5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 6], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 7], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]])], [([1, 5], [[1]]), ([3, 4], [[3], [2, 1], [1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 5], [[5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 6], [[6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 7], [[7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 8], [[8], [7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]])]]
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 fixtureActualExpectedOutcome
explicit oracle 0[][[1]]Failed
explicit oracle 1[[]][[]]Passed
explicit oracle 2[[7, 6, 2], [7, 5, 3], [7, 5, 2, 1], [7, 4, 3, 1], [6, 5, 4], [6, 5, 3, 1], [6, 4, 3, 2], [5, 4, 3, 2, 1]][[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]Failed
explicit oracle 3[[]][[]]Passed
explicit oracle 4[[]][[]]Passed
explicit oracle 5[[]][[]]Passed
explicit oracle 6[[]][[]]Passed
explicit oracle 7[[]][[]]Passed

SHA-256 / 6d424453e8c555553e7c22140ae5d45e75ba3b7ef5e52050d6244996cb7a968b

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,L=x;out=[]
    def visit(rem,hi,prefix):
     if rem==0:
      out.append(prefix);return
     for part in range(min(rem,hi),0,-1):
      if part<=0:continue
      visit(rem-part,part,prefix+[part])
    visit(n,L,[])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([0, 2], [[]]), ([0, 3], [[]]), ([0, 4], [[]]), ([0, 5], [[]]), ([0, 6], [[]])], [([1, 2], [[1]]), ([2, 3], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([2, 2], [[2], [1, 1]]), ([2, 4], [[2], [1, 1]]), ([2, 5], [[2], [1, 1]]), ([2, 6], [[2], [1, 1]])], [([1, 3], [[1]]), ([2, 6], [[2], [1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([4, 3], [[3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 4], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 5], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]), ([4, 6], [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]])], [([1, 4], [[1]]), ([3, 1], [[1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([6, 4], [[4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 5], [[5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 6], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]), ([6, 7], [[6], [5, 1], [4, 2], [4, 1, 1], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]])], [([1, 5], [[1]]), ([3, 4], [[3], [2, 1], [1, 1, 1]]), ([0, 1], [[]]), ([15, 8], [[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 5], [[5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 6], [[6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 7], [[7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]), ([8, 8], [[8], [7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [5, 1, 1, 1], [4, 4], [4, 3, 1], [4, 2, 2], [4, 2, 1, 1], [4, 1, 1, 1, 1], [3, 3, 2], [3, 3, 1, 1], [3, 2, 2, 1], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 2], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]])]]
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 fixtureActualExpectedOutcome
explicit oracle 0[[1]][[1]]Passed
explicit oracle 1[[]][[]]Passed
explicit oracle 2[[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]][[8, 7], [8, 6, 1], [8, 5, 2], [8, 5, 1, 1], [8, 4, 3], [8, 4, 2, 1], [8, 4, 1, 1, 1], [8, 3, 3, 1], [8, 3, 2, 2], [8, 3, 2, 1, 1], [8, 3, 1, 1, 1, 1], [8, 2, 2, 2, 1], [8, 2, 2, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [7, 7, 1], [7, 6, 2], [7, 6, 1, 1], [7, 5, 3], [7, 5, 2, 1], [7, 5, 1, 1, 1], [7, 4, 4], [7, 4, 3, 1], [7, 4, 2, 2], [7, 4, 2, 1, 1], [7, 4, 1, 1, 1, 1], [7, 3, 3, 2], [7, 3, 3, 1, 1], [7, 3, 2, 2, 1], [7, 3, 2, 1, 1, 1], [7, 3, 1, 1, 1, 1, 1], [7, 2, 2, 2, 2], [7, 2, 2, 2, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 3], [6, 6, 2, 1], [6, 6, 1, 1, 1], [6, 5, 4], [6, 5, 3, 1], [6, 5, 2, 2], [6, 5, 2, 1, 1], [6, 5, 1, 1, 1, 1], [6, 4, 4, 1], [6, 4, 3, 2], [6, 4, 3, 1, 1], [6, 4, 2, 2, 1], [6, 4, 2, 1, 1, 1], [6, 4, 1, 1, 1, 1, 1], [6, 3, 3, 3], [6, 3, 3, 2, 1], [6, 3, 3, 1, 1, 1], [6, 3, 2, 2, 2], [6, 3, 2, 2, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5], [5, 5, 4, 1], [5, 5, 3, 2], [5, 5, 3, 1, 1], [5, 5, 2, 2, 1], [5, 5, 2, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1], [5, 4, 4, 2], [5, 4, 4, 1, 1], [5, 4, 3, 3], [5, 4, 3, 2, 1], [5, 4, 3, 1, 1, 1], [5, 4, 2, 2, 2], [5, 4, 2, 2, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 3, 3, 3, 1], [5, 3, 3, 2, 2], [5, 3, 3, 2, 1, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 2, 2], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 3], [4, 4, 4, 2, 1], [4, 4, 4, 1, 1, 1], [4, 4, 3, 3, 1], [4, 4, 3, 2, 2], [4, 4, 3, 2, 1, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 3, 3, 3, 2], [4, 3, 3, 3, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]Passed
explicit oracle 3[[]][[]]Passed
explicit oracle 4[[]][[]]Passed
explicit oracle 5[[]][[]]Passed
explicit oracle 6[[]][[]]Passed
explicit oracle 7[[]][[]]Passed

SHA-256 / 3b65956913e269ad7d00acb9cbc5e7aa9623fa2a52f81821bd46658311b74d98

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 2026-09-29T14:39:25.214355+00:00.

Case digest / a6363f80e0d46c3c7d6c5407b464a530602d5bd9c1c49fb16b6cc263c9602a1a