FA-15266 / Numerics / Open access

Integer partition enumeration: partition candidate order · case 01

The exact integer partition enumeration result violates the stated contract at partition candidate order.

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

ROOT CAUSE

The partition candidate order step uses range(1,min(rem,hi)+1) instead of range(min(rem,hi),0,-1).

VERIFIED REPAIR

Use range(min(rem,hi),0,-1) at the partition candidate order step.

Unsuccessful approach: The partial repair range(min(rem,hi)-1,0,-1) still violates the partition candidate order 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(1,min(rem,hi)+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 = [[([2, 2], [[2], [1, 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]]), ([0, 2], [[]]), ([0, 3], [[]]), ([0, 4], [[]]), ([0, 5], [[]])], [([2, 3], [[2], [1, 1]]), ([1, 4], [[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]])], [([2, 4], [[2], [1, 1]]), ([1, 7], [[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]])], [([2, 5], [[2], [1, 1]]), ([2, 2], [[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]]), ([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]])], [([2, 6], [[2], [1, 1]]), ([2, 5], [[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]]), ([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 fixture	Actual	Expected	Outcome
explicit oracle 0	`[[1, 1], [2]]`	`[[2], [1, 1]]`	Failed
explicit oracle 1	`[[1]]`	`[[1]]`	Passed
explicit oracle 2	`[[]]`	`[[]]`	Passed
explicit oracle 3	[[1, 1, 1, 1, 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], [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 1, 1, 1, 1, 1, 1], [3, 2, 2, 2, 2, 1, 1, 1, 1], [3, 2, 2, 2, 2, 2, 1, 1], [3, 2, 2, 2, 2, 2, 2], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, 2, 1, 1, 1, 1, 1, 1, 1], [3, 3, 2, 2, 1, 1, 1, 1, 1], [3, 3, 2, 2, 2, 1, 1, 1], [3, 3, 2, 2, 2, 2, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 3, 2, 1, 1, 1, 1], [3, 3, 3, 2, 2, 1, 1], [3, 3, 3, 2, 2, 2], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 3, 2, 1], [3, 3, 3, 3, 3], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 1, 1, 1, 1, 1, 1, 1], [4, 2, 2, 2, 1, 1, 1, 1, 1], [4, 2, 2, 2, 2, 1, 1, 1], [4, 2, 2, 2, 2, 2, 1], [4, 3, 1, 1, 1, 1, 1, 1, 1, 1], [4, 3, 2, 1, 1, 1, 1, 1, 1], [4, 3, 2, 2, 1, 1, 1, 1], [4, 3, 2, 2, 2, 1, 1], [4, 3, 2, 2, 2, 2], [4, 3, 3, 1, 1, 1, 1, 1], [4, 3, 3, 2, 1, 1, 1], [4, 3, 3, 2, 2, 1], [4, 3, 3, 3, 1, 1], [4, 3, 3, 3, 2], [4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 2, 1, 1, 1, 1, 1], [4, 4, 2, 2, 1, 1, 1], [4, 4, 2, 2, 2, 1], [4, 4, 3, 1, 1, 1, 1], [4, 4, 3, 2, 1, 1], [4, 4, 3, 2, 2], [4, 4, 3, 3, 1], [4, 4, 4, 1, 1, 1], [4, 4, 4, 2, 1], [4, 4, 4, 3], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 2, 1, 1, 1, 1, 1, 1, 1, 1], [5, 2, 2, 1, 1, 1, 1, 1, 1], [5, 2, 2, 2, 1, 1, 1, 1], [5, 2, 2, 2, 2, 1, 1], [5, 2, 2, 2, 2, 2], [5, 3, 1, 1, 1, 1, 1, 1, 1], [5, 3, 2, 1, 1, 1, 1, 1], [5, 3, 2, 2, 1, 1, 1], [5, 3, 2, 2, 2, 1], [5, 3, 3, 1, 1, 1, 1], [5, 3, 3, 2, 1, 1], [5, 3, 3, 2, 2], [5, 3, 3, 3, 1], [5, 4, 1, 1, 1, 1, 1, 1], [5, 4, 2, 1, 1, 1, 1], [5, 4, 2, 2, 1, 1], [5, 4, 2, 2, 2], [5, 4, 3, 1, 1, 1], [5, 4, 3, 2, 1], [5, 4, 3, 3], [5, 4, 4, 1, 1], [5, 4, 4, 2], [5, 5, 1, 1, 1, 1, 1], [5, 5, 2, 1, 1, 1], [5, 5, 2, 2, 1], [5, 5, 3, 1, 1], [5, 5, 3, 2], [5, 5, 4, 1], [5, 5, 5], [6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 2, 1, 1, 1, 1, 1, 1, 1], [6, 2, 2, 1, 1, 1, 1, 1], [6, 2, 2, 2, 1, 1, 1], [6, 2, 2, 2, 2, 1], [6, 3, 1, 1, 1, 1, 1, 1], [6, 3, 2, 1, 1, 1, 1], [6, 3, 2, 2, 1, 1], [6, 3, 2, 2, 2], [6, 3, 3, 1, 1, 1], [6, 3, 3, 2, 1], [6, 3, 3, 3], [6, 4, 1, 1, 1, 1, 1], [6, 4, 2, 1, 1, 1], [6, 4, 2, 2, 1], [6, 4, 3, 1, 1], [6, 4, 3, 2], [6, 4, 4, 1], [6, 5, 1, 1, 1, 1], [6, 5, 2, 1, 1], [6, 5, 2, 2], [6, 5, 3, 1], [6, 5, 4], [6, 6, 1, 1, 1], [6, 6, 2, 1], [6, 6, 3], [7, 1, 1, 1, 1, 1, 1, 1, 1], [7, 2, 1, 1, 1, 1, 1, 1], [7, 2, 2, 1, 1, 1, 1], [7, 2, 2, 2, 1, 1], [7, 2, 2, 2, 2], [7, 3, 1, 1, 1, 1, 1], [7, 3, 2, 1, 1, 1], [7, 3, 2, 2, 1], [7, 3, 3, 1, 1], [7, 3, 3, 2], [7, 4, 1, 1, 1, 1], [7, 4, 2, 1, 1], [7, 4, 2, 2], [7, 4, 3, 1], [7, 4, 4], [7, 5, 1, 1, 1], [7, 5, 2, 1], [7, 5, 3], [7, 6, 1, 1], [7, 6, 2], [7, 7, 1], [8, 1, 1, 1, 1, 1, 1, 1], [8, 2, 1, 1, 1, 1, 1], [8, 2, 2, 1, 1, 1], [8, 2, 2, 2, 1], [8, 3, 1, 1, 1, 1], [8, 3, 2, 1, 1], [8, 3, 2, 2], [8, 3, 3, 1], [8, 4, 1, 1, 1], [8, 4, 2, 1], [8, 4, 3], [8, 5, 1, 1], [8, 5, 2], [8, 6, 1], [8, 7]]	[[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 4	`[[]]`	`[[]]`	Passed
explicit oracle 5	`[[]]`	`[[]]`	Passed
explicit oracle 6	`[[]]`	`[[]]`	Passed
explicit oracle 7	`[[]]`	`[[]]`	Passed

SHA-256 / 0b03fc4a8c0a7c7995d1ae9a68c56dc945c0f6559cb4a3082c7517c1772ebdd9

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)-1,0,-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 = [[([2, 2], [[2], [1, 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]]), ([0, 2], [[]]), ([0, 3], [[]]), ([0, 4], [[]]), ([0, 5], [[]])], [([2, 3], [[2], [1, 1]]), ([1, 4], [[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, 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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]])], [([2, 6], [[2], [1, 1]]), ([2, 5], [[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]]), ([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 fixture	Actual	Expected	Outcome
explicit oracle 0	`[]`	`[[2], [1, 1]]`	Failed
explicit oracle 1	`[]`	`[[1]]`	Failed
explicit oracle 2	`[[]]`	`[[]]`	Passed
explicit oracle 3	`[]`	[[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 4	`[[]]`	`[[]]`	Passed
explicit oracle 5	`[[]]`	`[[]]`	Passed
explicit oracle 6	`[[]]`	`[[]]`	Passed
explicit oracle 7	`[[]]`	`[[]]`	Passed

SHA-256 / 74ab81cb73553280b34922e66cafd6feee80db7e88647628b7862b5ad709a3f7

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 = [[([2, 2], [[2], [1, 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, 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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]])], [([2, 6], [[2], [1, 1]]), ([2, 5], [[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]]), ([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 fixture	Actual	Expected	Outcome
explicit oracle 0	`[[2], [1, 1]]`	`[[2], [1, 1]]`	Passed
explicit oracle 1	`[[1]]`	`[[1]]`	Passed
explicit oracle 2	`[[]]`	`[[]]`	Passed
explicit oracle 3	[[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 4	`[[]]`	`[[]]`	Passed
explicit oracle 5	`[[]]`	`[[]]`	Passed
explicit oracle 6	`[[]]`	`[[]]`	Passed
explicit oracle 7	`[[]]`	`[[]]`	Passed

SHA-256 / b3e064d6a3dee3426b5ec2f142aed72e4374aa9dd1a2cd4d1b7bc5cfb35f381c

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 2026-09-29T14:39:25.031006+00:00.

Case digest / 57e26ff91ca166b5006f0950222c64e113a5b0b4d74e2ed4b8d15e04f223259f