broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    sources={}
    counts={x:0 for x in full}
    mode='union'
    out=[]
    for cmd in commands:
        op=cmd[0]
        if op in ('put','move','remove'):
            key=cmd[1]
            old=sources.get(key,set())
            for x in old & full: counts[x]-=1
            if op=='put': new=set(cmd[2])
            elif op=='move': new={x+cmd[2] for x in old}
            else: new=set()
            if op=='remove': sources.pop(key,None)
            else: sources[key]=new
            for x in new & full: counts[x]+=1
        elif op=='mode': mode=cmd[1]
        elif op=='draw':
            if mode=='union': selected=[x for x in full if counts[x]>0]
            elif mode=='single': selected=[x for x in full if counts[x]==1]
            elif mode=='overlap': selected=[x for x in full if counts[x]>=2]
            else: selected=[x for x in full if counts[x]==1]
            out.append(sorted(selected))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 4), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 4), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 4), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 4), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 4), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 4), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 4), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 4), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 4), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 4), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 4), [[0, 1, 2, 3]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 4), [[0, 1]])
if N == 2:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 5), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 5), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 5), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 5), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 5), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 5), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 5), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 5), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 5), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 5), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 5), [[0, 1]])
if N == 3:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 6), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 6), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 6), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 6), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 6), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 6), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 6), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 6), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 6), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 6), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 6), [[0, 1]])
if N == 4:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 7), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 7), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 7), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 7), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 7), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 7), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 7), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 7), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 7), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 7), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 7), [[0, 1]])
if N == 5:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 8), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 8), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 8), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 8), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 8), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 8), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 8), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 8), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 8), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 8), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 8), [[0, 1]])
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    sources={}
    counts={x:0 for x in full}
    mode='union'
    out=[]
    for cmd in commands:
        op=cmd[0]
        if op in ('put','move','remove'):
            key=cmd[1]
            old=sources.get(key,set())
            for x in old & full: counts[x]-=1
            if op=='put': new=set(cmd[2])
            elif op=='move': new={x+cmd[2] for x in old}
            else: new=set()
            if op=='remove': sources.pop(key,None)
            else: sources[key]=new
            for x in new & full: counts[x]+=1
        elif op=='mode': mode=cmd[1]
        elif op=='draw':
            if mode=='union': selected=[x for x in full if counts[x]>0]
            elif mode=='single': selected=[x for x in full if counts[x]==1]
            elif mode=='overlap': selected=[x for x in full if counts[x]>=2]
            else: selected=[x for x in full if counts[x]>0]
            out.append(sorted(selected))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 4), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 4), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 4), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 4), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 4), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 4), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 4), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 4), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 4), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 4), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 4), [[0, 1, 2, 3]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 4), [[0, 1]])
if N == 2:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 5), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 5), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 5), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 5), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 5), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 5), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 5), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 5), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 5), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 5), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 5), [[0, 1]])
if N == 3:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 6), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 6), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 6), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 6), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 6), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 6), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 6), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 6), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 6), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 6), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 6), [[0, 1]])
if N == 4:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 7), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 7), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 7), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 7), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 7), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 7), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 7), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 7), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 7), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 7), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 7), [[0, 1]])
if N == 5:
    check('explicit sequence 0', solve([['put', 'a', [0, 1]], ['put', 'a', [2]], ['draw']], 8), [[2]])
    check('explicit sequence 1', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['draw']], 8), [[0]])
    check('explicit sequence 2', solve([['put', 'a', [-1]], ['move', 'a', 2], ['draw']], 8), [[1]])
    check('explicit sequence 3', solve([['put', 'a', [2]], ['move', 'a', -1], ['draw']], 8), [[1]])
    check('explicit sequence 4', solve([['put', 'a', [0]], ['put', 'b', [0]], ['remove', 'a'], ['remove', 'a'], ['draw']], 8), [[0]])
    check('explicit sequence 5', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'overlap'], ['draw']], 8), [[0]])
    check('explicit sequence 6', solve([['put', 'a', [0]], ['mode', 'single'], ['draw']], 8), [[0]])
    check('explicit sequence 7', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'single'], ['draw']], 8), [[]])
    check('explicit sequence 8', solve([['put', 'a', [0]], ['put', 'b', [0]], ['put', 'c', [0]], ['mode', 'overlap'], ['draw'], ['mode', 'odd'], ['draw']], 8), [[0], [0]])
    check('explicit sequence 9', solve([['put', 'a', [0]], ['put', 'b', [0]], ['mode', 'odd'], ['draw']], 8), [[]])
    check('explicit sequence 10', solve([['put', 'a', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]], ['draw']], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 11', solve([['put', 'a', [0, 1]], ['put', 'b', [1]], ['draw']], 8), [[0, 1]])
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)

prompt:
Odd clipping rejects triple coverage.

Sources contribute unique sample sets to an overlap-count clip. Replacing a source first removes its old contribution. Removing an unknown source is inert. Coverage may select union, exactly-one, at-least-two or odd count. Moving a source translates its retained original sample set before clipping to the target, allowing previously exterior samples to enter. Draw emits selected finite samples.

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not body: continue
            before=segments[i-1][4] if i>0 else (segments[-1][4] if closed and count else False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

meaning: Fixture-count band, not measured model difficulty

deps: stdlib

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not active and not body: continue
            before=segments[i-1][4] if i>0 else (segments[-1][4] if closed and count else False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

prompt:
Inactive dash segments are rasterized whenever their body samples are nonempty.

Segments carry precomputed body, start-cap, end-cap and following-join sample sets plus an active flag. Active adjacent segments share a join and suppress interior caps. Inactive segments create dash gaps; each active component receives caps at its gap endpoints. A closed path connects the last and first segments. Empty bodies may still have cap coverage. Clip the complete union to the requested mask and target.

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not active or not body: continue
            before=segments[i-1][4] if i>0 else (segments[-1][4] if closed and count else False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not active or (not body and not start): continue
            before=segments[i-1][4] if i>0 else (segments[-1][4] if closed and count else False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

prompt:
An active zero-length segment loses precomputed round-cap coverage.

Segments carry precomputed body, start-cap, end-cap and following-join sample sets plus an active flag. Active adjacent segments share a join and suppress interior caps. Inactive segments create dash gaps; each active component receives caps at its gap endpoints. A closed path connects the last and first segments. Empty bodies may still have cap coverage. Clip the complete union to the requested mask and target.

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not active: continue
            before=segments[i-1][4] if i>0 else (False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    full=set(range(size))
    out=[]
    for segments,closed,clip in commands:
        coverage=set()
        count=len(segments)
        for i,(body,start,end,join,active) in enumerate(segments):
            if not active: continue
            before=segments[i-1][4] if i>0 else (segments[-1][4] if closed and count>2 else False)
            after=segments[i+1][4] if i+1<count else (segments[0][4] if closed and count else False)
            coverage.update(body)
            if not before: coverage.update(start)
            if not after: coverage.update(end)
            if after: coverage.update(join)
        out.append(sorted(coverage & set(clip) & full))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 4), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 4), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 4), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 4), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 4), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 4), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 4), [[0, 1, 2, 3]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 4), [[0, 1, 3]])
if N == 2:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 5), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 5), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 5), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 5), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 5), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 5), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 5), [[0, 1, 2, 3, 4]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 5), [[0, 1, 3]])
if N == 3:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 6), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 6), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 6), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 6), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 6), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 6), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 6), [[0, 1, 2, 3, 4, 5]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 6), [[0, 1, 3]])
if N == 4:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 7), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 7), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 7), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 7), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 7), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 7), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 7), [[0, 1, 2, 3, 4, 5, 6]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 7), [[0, 1, 3]])
if N == 5:
    check('explicit sequence 0', solve([[[[[0], [1], [2], [3], False]], False, [0, 1, 2, 3]]], 8), [[]])
    check('explicit sequence 1', solve([[[[[], [0], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 2', solve([[[[[], [], [1], [], True]], False, [0, 1, 2, 3]]], 8), [[1]])
    check('explicit sequence 3', solve([[[[[0], [2], [3], [1], True], [[1], [2], [3], [0], True]], True, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 4', solve([[[[[0], [1], [2], [3], True], [[], [], [], [], False], [[1], [2], [3], [0], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2, 3]])
    check('explicit sequence 5', solve([[[[[0], [], [1], [2], True], [[], [], [], [], False], [[], [], [], [], False], [[], [], [], [], False]], False, [0, 1, 2, 3]]], 8), [[0, 1]])
    check('explicit sequence 6', solve([[[[[0], [1], [2], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 7', solve([[[[[0], [], [], [2], True], [[1], [], [], [3], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 2]])
    check('explicit sequence 8', solve([[[[[0], [], [], [2], True], [[], [], [], [], False]], True, [0, 1, 2, 3]]], 8), [[0]])
    check('explicit sequence 9', solve([[[[[0, 1], [2], [3], [], True]], False, [0]]], 8), [[0]])
    check('explicit sequence 10', solve([[[[[0, 1], [2], [3], [], True]], False, []]], 8), [[]])
    check('explicit sequence 11', solve([[[[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [], [], [], True]], False, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]], 8), [[0, 1, 2, 3, 4, 5, 6, 7]])
    check('explicit sequence 12', solve([[[[[0], [], [], [], True], [[], [], [], [], False], [[1], [3], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
    check('explicit sequence 13', solve([[[[[0], [1], [2], [3], True], [[0], [], [], [], True]], False, [0, 1, 2, 3]]], 8), [[0, 1, 3]])
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)

prompt:
A closed path emits an open start cap at its seam.

Segments carry precomputed body, start-cap, end-cap and following-join sample sets plus an active flag. Active adjacent segments share a join and suppress interior caps. Inactive segments create dash gaps; each active component receives caps at its gap endpoints. A closed path connects the last and first segments. Empty bodies may still have cap coverage. Clip the complete union to the requested mask and target.

split: open-access