tasks/program-execution-tracing/contexts/sample-00021.md

### 001

```python
def f1(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    levels = {start: 0} if limit > 0 or limit < 0 else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    pending.append(nxt)
    sequence = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f1([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 002

```python
def f2(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    groups = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f2(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 003

```python
def f3(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    levels = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in levels and (not nxt.startswith('Z')):
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    listing = list(levels)
    lastlevel = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': listing, 'depth': levels, 'frontier': lastlevel, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f3([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 004

```python
def f4(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f4([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 005

```python
def f5(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f5([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 006

```python
def f6(left, right, banned):
    left = list(left)

    def normalize(value):
        return str(value).strip().upper()[:12]
    banned = {normalize(value) for value in banned}
    a = {normalize(value) for value in left if normalize(value) != normalize(value) or normalize(value) != ''} - banned
    b = {normalize(value) for value in right} - banned
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f6(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 007

```python
def f7(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f7([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 008

```python
def f8(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in frequency.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f8(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 009

```python
def f9(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f9([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 010

```python
def f10(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f10([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 011

```python
def f11(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f11([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 012

```python
def f12(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f12(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 013

```python
def f13(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    rootsource = dict(incoming)
    finished = set()
    listing = []
    rounds = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f13(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 014

```python
def f14(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f14([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 015

```python
def f15(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not segments or left > segments[-1][1] + gap % 5:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    gaps = []
    for pos in range(1, min(50, len(segments))):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f15([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 016

```python
def f16(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \n').upper()
    excluded = {str(value).strip() for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right if normalize(value) != ''} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f16(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 017

```python
def f17(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    finished = set()
    listing = []
    rounds = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished))
        if not available:
            break
        current = available[:1] if any((str(node).isupper() for node in nodes)) else available
        rounds.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in nextmap[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': listing, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f17(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 018

```python
def f18(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    finished = set()
    sequence = []
    rounds = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        rounds.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f18(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 019

```python
def f19(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f19([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 020

```python
def f20(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f20(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 021

```python
def f21(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in repeats:
                repeats.append(list(point))
            found.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f21([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 022

```python
def f22(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    startdegree = dict(indegree)
    finished = set()
    result = []
    rounds = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available[:1] if any((str(node).isupper() for node in nodes)) else available
        rounds.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': rounds, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f22(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 023

```python
def f23(left, right, excluded):
    left = list(left)

    def canon(value):
        return str(value).strip().upper()[:12]
    excluded = {str(value).upper() for value in excluded}
    a = {canon(value) for value in left if canon(value) != canon(value) or canon(value) != ''} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f23(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 024

```python
def f24(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' ').upper()
    excluded = {str(value).upper() for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f24(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 025

```python
def f25(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            pending = [(row, col)]
            visited.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        pending.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f25(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 026

```python
def f26(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f26(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 027

```python
def f27(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in repeats:
                repeats.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f27([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 028

```python
def f28(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f28([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 029

```python
def f29(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    ranking = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in tallies.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in ranking[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f29(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 030

```python
def f30(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not segments or left > segments[-1][1] + min(gap, 2):
            segments.append([left, right])
        else:
            segments[-1][1] = max(0, segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f30([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 031

```python
def f31(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    handled = set()
    listing = []
    groups = []
    while len(handled) < len(nodes) and len(handled) < 20:
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in handled), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            handled.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f31(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 032

```python
def f32(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    items = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f32(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 033

```python
def f33(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        routes.setdefault(a, []).append(b)
    levels = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in (node for node in sorted(routes.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    sequence = list(levels)
    lastlevel = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': lastlevel, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f33([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 034

```python
def f34(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop or len(word) < 2:
            continue
        wordmap[word] = min(9, wordmap.get(word, 0) + 1)
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f34(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 035

```python
def f35(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    sequence = list(levels)
    lastlevel = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': lastlevel, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f35([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 036

```python
def f36(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    listing = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': listing, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f36([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 037

```python
def f37(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y = max(-64, min(64, y + dy))
            used = min(64, used + 1)
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f37([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 038

```python
def f38(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0} if limit > 0 or limit < 0 else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    work.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f38([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 039

```python
def f39(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in crossings:
                crossings.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f39([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 040

```python
def f40(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f40([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 041

```python
def f41(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap % 5:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f41([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 042

```python
def f42(left, right, excluded):
    left = list(left)

    def canon(value):
        return str(value).strip(' \r').upper()
    excluded = {canon(value) for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f42(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 043

```python
def f43(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        queue.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f43(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 044

```python
def f44(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f44([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 045

```python
def f45(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f45([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 046

```python
def f46(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap:
            result.append([left, right])
        else:
            result[-1][1] = right
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f46([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 047

```python
def f47(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f47(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 048

```python
def f48(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(totals[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f48([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 049

```python
def f49(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' ').upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right if normalize(value) != ''} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f49(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 050

```python
def f50(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted((pair for pair in spans if pair[0] <= pair[1])):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, min(50, len(combined))):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': min(100, max((right - left for left, right in combined)))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f50([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 051

```python
def f51(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    sorteditems = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f51(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 052

```python
def f52(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    pending.append(nxt)
    sequence = list(levels)
    edge = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': edge, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f52([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 053

```python
def f53(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges[:16]:
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    edge = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': edge[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f53([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 054

```python
def f54(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f54([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 055

```python
def f55(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in found and list(point) not in repeats:
                repeats.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f55([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 056

```python
def f56(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted((pair for pair in spans if pair[0] < pair[1] or pair[0] != pair[1])):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(min(100, left - combined[pos - 1][1]))
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f56([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 057

```python
def f57(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    sequence = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f57([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 058

```python
def f58(board):
    board = list(board)
    found = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(min(len(board[row]), 10)):
            if col >= 12 or board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f58(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 059

```python
def f59(board):
    board = list(board)
    found = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f59(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 060

```python
def f60(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + max(0, gap):
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f60([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 061

```python
def f61(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f61([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 062

```python
def f62(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    steps = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    sequence = list(steps)
    edge = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': edge, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f62([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 063

```python
def f63(left, right, excluded):
    left = list(left)

    def tidy(value):
        return str(value).strip().upper()
    excluded = {tidy(value) for value in excluded}
    a = {tidy(value) for value in left if tidy(value) != tidy(value) or tidy(value) != ''} - excluded
    b = {tidy(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f63(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 064

```python
def f64(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = max(0, combined[-1][1], right)
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f64([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 065

```python
def f65(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans):
        if not segments or left > segments[-1][1] + gap % 5:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f65([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 066

```python
def f66(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in (node for node in sorted(routes.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    work.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f66([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 067

```python
def f67(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    groups = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f67(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 068

```python
def f68(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap:
            result.append([left, right])
        else:
            result[-1][1] = max(0, result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f68([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 069

```python
def f69(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f69(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 070

```python
def f70(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        frequency[word] = min(9, frequency.get(word, 0) + 1)
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f70(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 071

```python
def f71(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    ordered = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in tallies.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f71(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 072

```python
def f72(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in found and list(point) not in crossings:
                crossings.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f72([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 073

```python
def f73(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f73([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 074

```python
def f74(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in found and list(point) not in repeats:
                repeats.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f74([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 075

```python
def f75(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x = max(-64, min(64, x + dx))
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f75([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 076

```python
def f76(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum((max(item, 0) for item in values[pos:pos + size])))
    indexes = [pos for pos, value in enumerate(totals) if value >= limit]
    growth = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max([0] + totals), 'hits': indexes, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f76([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 077

```python
def f77(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges:
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0} if any((start in edge for edge in edges)) else {} if limit > 0 or limit < 0 else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f77([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 078

```python
def f78(left, right, banned):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \n').upper()
    banned = {normalize(value) for value in banned}
    a = {normalize(value) for value in left if normalize(value) != normalize(value) or normalize(value) != ''} - banned
    b = {normalize(value) for value in right} - banned
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f78(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 079

```python
def f79(board):
    board = list(board)
    known = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            work = [(row, col)]
            known.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f79(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 080

```python
def f80(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ranking = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ranking[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f80(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 081

```python
def f81(board):
    board = list(board)
    found = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        if len(found) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f81(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 082

```python
def f82(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans, key=lambda pair: pair[0]):
        if not result or left > result[-1][1] + min(gap, 2):
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, min(50, len(result))):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f82([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 083

```python
def f83(left, right, ignored):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \r').upper()
    ignored = {str(value).upper() for value in ignored}
    a = {normalize(value) for value in left} - ignored
    b = {normalize(value) for value in right} - ignored
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f83(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 084

```python
def f84(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    distance = {start: 0} if any((start in edge for edge in edges)) else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f84([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 085

```python
def f85(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = right
    gaps = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f85([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 086

```python
def f86(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f86([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 087

```python
def f87(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    levels = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    listing = list(levels)
    edge = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': listing, 'depth': levels, 'frontier': edge[:3], 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f87([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 088

```python
def f88(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    terms = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop or len(word) > 12:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f88(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 089

```python
def f89(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f89([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 090

```python
def f90(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f90(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 091

```python
def f91(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ranking = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ranking[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f91(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 092

```python
def f92(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + min(gap, 2):
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    gaps = []
    for pos in range(1, min(50, len(combined))):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f92([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 093

```python
def f93(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    sequence = list(steps)
    furthest = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': furthest, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f93([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 094

```python
def f94(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + max(0, gap):
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    spaces = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        spaces.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': spaces, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f94([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 095

```python
def f95(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in repeats:
                repeats.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f95([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 096

```python
def f96(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f96(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 097

```python
def f97(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    startdegree = dict(indegree)
    complete = set()
    sequence = []
    groups = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in complete), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f97(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 098

```python
def f98(left, right, ignored):
    left = list(left)

    def normalize(value):
        return ' '.join(str(value).split()).upper()
    ignored = {normalize(value) for value in ignored}
    a = {normalize(value) for value in left if normalize(value) != normalize(value) or normalize(value) != ''} - ignored
    b = {normalize(value) for value in right if normalize(value) != ''} - ignored
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f98(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 099

```python
def f99(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    listing = []
    layers = []
    while len(complete) < len(nodes) and len(complete) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in complete))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            listing.append(node)
        for node in current:
            for nxt in routes[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f99(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 100

```python
def f100(board):
    board = list(board)
    known = set()
    components = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            queue = [(row, col)]
            known.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f100(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 101

```python
def f101(board):
    board = list(board)
    known = set()
    regions = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            pending = [(row, col)]
            known.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        pending.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f101(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 102

```python
def f102(left, right, ignored):
    left = list(left)

    def tidy(value):
        return str(value).strip().upper()
    ignored = {str(value).upper() for value in ignored}
    a = {tidy(value) for value in left} - ignored
    b = {tidy(value) for value in right} - ignored
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f102(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 103

```python
def f103(board):
    board = list(board)
    found = set()
    pieces = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            pieces.append((len(cells), min(cells)))
    pieces.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in pieces], 'anchors': [list(anchor) for size, anchor in pieces], 'filled': sum((size for size, anchor in pieces)), 'count': len(pieces)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f103(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 104

```python
def f104(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ranking = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ranking[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f104(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 105

```python
def f105(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f105([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 106

```python
def f106(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in frequency.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f106(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 107

```python
def f107(left, right, excluded):
    left = list(left)

    def normalize(value):
        return ' '.join(str(value).split()).upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left if normalize(value) != normalize(value) or normalize(value) != ''} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f107(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 108

```python
def f108(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    sorteditems = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f108(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 109

```python
def f109(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    result = []
    rounds = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in complete), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        rounds.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in routes[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': result, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f109(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 110

```python
def f110(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = right
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((min(100, right - left) for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f110([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 111

```python
def f111(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f111([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 112

```python
def f112(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f112(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 113

```python
def f113(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    handled = set()
    sequence = []
    rounds = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if needs[node] == 0 and node not in handled), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f113(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 114

```python
def f114(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f114([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 115

```python
def f115(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f115([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 116

```python
def f116(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f116(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 117

```python
def f117(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f117(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 118

```python
def f118(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    startdegree = dict(indegree)
    handled = set()
    listing = []
    layers = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in handled))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f118(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 119

```python
def f119(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        nextmap[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    sequence = []
    layers = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in complete), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f119(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 120

```python
def f120(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \n').upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f120(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 121

```python
def f121(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap + 1:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f121([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 122

```python
def f122(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f122([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 123

```python
def f123(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    rootsource = dict(incoming)
    finished = set()
    listing = []
    rounds = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f123(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 124

```python
def f124(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f124([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 125

```python
def f125(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f125([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 126

```python
def f126(left, right, banned):
    left = list(left)

    def normalize(value):
        return str(value).strip().upper()[:12]
    banned = {normalize(value) for value in banned}
    a = {normalize(value) for value in left} - banned
    b = {normalize(value) for value in right if normalize(value) != ''} - banned
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f126(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 127

```python
def f127(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f127(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 128

```python
def f128(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f128([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 129

```python
def f129(left, right, banned):
    left = list(left)

    def canon(value):
        return ' '.join(str(value).split()).upper()
    banned = {str(value).upper() for value in banned}
    a = {canon(value) for value in left} - banned
    b = {canon(value) for value in right} - banned
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f129(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 130

```python
def f130(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    sequence = list(distance)
    lastlevel = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': lastlevel, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f130([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 131

```python
def f131(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    indexes = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f131([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 132

```python
def f132(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f132([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 133

```python
def f133(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \n').upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f133(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 134

```python
def f134(left, right, ignored):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \n').upper()
    ignored = {str(value).strip() for value in ignored}
    a = {normalize(value) for value in left} - ignored
    b = {normalize(value) for value in right} - ignored
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f134(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 135

```python
def f135(board):
    board = list(board)
    visited = set()
    pieces = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            pending = [(row, col)]
            visited.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        pending.append(nxt)
            pieces.append((len(cells), min(cells)))
    pieces.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in pieces], 'anchors': [list(anchor) for size, anchor in pieces], 'filled': sum((size for size, anchor in pieces)), 'count': len(pieces)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f135(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 136

```python
def f136(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted((pair for pair in spans if pair[0] < pair[1] or pair[0] != pair[1])):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = max(0, combined[-1][1], right)
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f136([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 137

```python
def f137(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip().upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f137(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 138

```python
def f138(left, right, excluded):
    left = list(left)

    def normalize(value):
        return ' '.join(str(value).split()).upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f138(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 139

```python
def f139(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in repeats:
                repeats.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f139([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 140

```python
def f140(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = min(9, frequency.get(word, 0) + 1)
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f140(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 141

```python
def f141(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            pending = [(row, col)]
            visited.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        pending.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f141(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 142

```python
def f142(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    windows = []
    for pos in range(min(64, len(values) - size + 1)):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f142([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 143

```python
def f143(left, right, banned):
    left = list(left)

    def tidy(value):
        return ' '.join(str(value).split()).upper()
    banned = {str(value).upper() for value in banned}
    a = {tidy(value) for value in left} - banned
    b = {tidy(value) for value in right} - banned
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f143(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 144

```python
def f144(board):
    board = list(board)
    known = set()
    regions = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            pending = [(row, col)]
            known.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        pending.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f144(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 145

```python
def f145(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f145([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 146

```python
def f146(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    handled = set()
    result = []
    layers = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in handled), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f146(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 147

```python
def f147(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(set(spans)):
        if not result or left > result[-1][1] + max(0, gap):
            result.append([left, right])
        else:
            result[-1][1] = right
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f147([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 148

```python
def f148(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f148(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 149

```python
def f149(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x = max(-64, min(64, x + dx))
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in visited and list(point) not in repeats:
                repeats.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f149([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 150

```python
def f150(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f150(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 151

```python
def f151(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    work.append(nxt)
    listing = list(distance)
    lastlevel = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': lastlevel, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f151([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 152

```python
def f152(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f152(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 153

```python
def f153(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(min(64, len(values) - size + 1)):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(windows) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f153([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 154

```python
def f154(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(totals) if value >= limit]
    growth = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': min(256, max(totals)), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f154([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 155

```python
def f155(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f155(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 156

```python
def f156(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f156([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 157

```python
def f157(left, right, excluded):
    left = list(left)

    def canon(value):
        return ' '.join(str(value).split()).upper()[:12]
    excluded = {canon(value) for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f157(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 158

```python
def f158(left, right, excluded):
    left = list(left)

    def canon(value):
        return ' '.join(str(value).split()).upper()[:12]
    excluded = {canon(value) for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right if canon(value) != ''} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f158(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 159

```python
def f159(board):
    board = list(board)
    found = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            work = [(row, col)]
            found.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f159(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 160

```python
def f160(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = min(9, frequency.get(word, 0) + 1)
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f160(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 161

```python
def f161(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ranking = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in frequency.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ranking[:5]], 'initials': starts, 'size': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f161(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 162

```python
def f162(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        work.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f162(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 163

```python
def f163(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans, key=lambda pair: (pair[1], pair[0])):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f163([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 164

```python
def f164(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in crossings:
                crossings.append(list(point))
            known.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f164([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 165

```python
def f165(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    pending.append(nxt)
    sequence = list(steps)
    furthest = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': furthest, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f165([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 166

```python
def f166(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f166([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 167

```python
def f167(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f167([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 168

```python
def f168(left, right, excluded):
    left = list(left)

    def tidy(value):
        return ' '.join(str(value).split()).upper()
    excluded = {str(value).upper() for value in excluded}
    a = {tidy(value) for value in left} - excluded
    b = {tidy(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f168(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 169

```python
def f169(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(totals) if value >= limit]
    growth = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': matches, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f169([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 170

```python
def f170(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f170(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 171

```python
def f171(board):
    board = list(board)
    found = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f171(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 172

```python
def f172(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f172(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 173

```python
def f173(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    distance = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    result = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f173([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 174

```python
def f174(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(series[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(series))) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max([0] + series), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f174([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 175

```python
def f175(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f175([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 176

```python
def f176(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(windows) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f176([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 177

```python
def f177(board):
    board = list(board)
    known = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            work = [(row, col)]
            known.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        work.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f177(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 178

```python
def f178(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f178([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 179

```python
def f179(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f179([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 180

```python
def f180(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(totals) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': min(256, max(totals)), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f180([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 181

```python
def f181(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    handled = set()
    sequence = []
    rounds = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in handled))
        if not nextbatch:
            break
        current = nextbatch
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f181(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 182

```python
def f182(left, right, excluded):
    left = list(left)

    def canon(value):
        return str(value).strip(' \r').upper()
    excluded = {str(value).upper() for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f182(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 183

```python
def f183(board):
    board = list(board)
    known = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            queue = [(row, col)]
            known.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f183(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 184

```python
def f184(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z' or (char == "'" and word):
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop or len(word) > 12:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f184(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 185

```python
def f185(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f185([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 186

```python
def f186(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    edge = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': edge, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f186([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 187

```python
def f187(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    work.append(nxt)
    result = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': result, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f187([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 188

```python
def f188(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        work.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f188(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 189

```python
def f189(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ranking = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ranking[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f189(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 190

```python
def f190(left, right, ignored):
    left = list(left)

    def canon(value):
        return str(value).strip(' \n').upper()
    ignored = {str(value).upper() for value in ignored}
    a = {canon(value) for value in left} - ignored
    b = {canon(value) for value in right} - ignored
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f190(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 191

```python
def f191(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ranking = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ranking[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f191(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 192

```python
def f192(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        routes.setdefault(a, []).append(b)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in (node for node in sorted(routes.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    result = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': result, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f192([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 193

```python
def f193(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(totals) if value >= limit]
    increases = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f193([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 194

```python
def f194(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    sequence = []
    layers = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in complete), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f194(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 195

```python
def f195(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {str(word) for word in stop}
    terms = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    sorteditems = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f195(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 196

```python
def f196(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(totals) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] >= totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f196([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 197

```python
def f197(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f197([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 198

```python
def f198(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x = max(-64, min(64, x + dx))
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f198([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 199

```python
def f199(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + min(gap, 2):
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((min(100, right - left) for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f199([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 200

```python
def f200(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = right
    spaces = []
    for pos in range(1, min(50, len(combined))):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f200([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 201

```python
def f201(left, right, ignored):
    left = list(left)

    def normalize(value):
        return ' '.join(str(value).split()).upper()
    ignored = {normalize(value) for value in ignored}
    a = {normalize(value) for value in left} - ignored
    b = {normalize(value) for value in right} - ignored
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f201(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 202

```python
def f202(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans, key=lambda pair: pair[0]):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    spaces = []
    for pos in range(1, min(50, len(segments))):
        left = segments[pos][0]
        spaces.append(min(100, left - segments[pos - 1][1]))
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f202([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 203

```python
def f203(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes):
        available = sorted((node for node in nodes if needs[node] == 0 and node not in handled), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f203(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 204

```python
def f204(left, right, ignored):
    left = list(left)

    def canon(value):
        return str(value).strip(' ').upper()
    ignored = {canon(value) for value in ignored}
    a = {canon(value) for value in left} - ignored
    b = {canon(value) for value in right} - ignored
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f204(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 205

```python
def f205(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    distance = {start: 0} if limit > 0 or limit < 0 else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    result = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': furthest[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f205([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 206

```python
def f206(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    complete = set()
    result = []
    layers = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in complete))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f206(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 207

```python
def f207(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.setdefault(a, []).append(b)
    levels = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    result = list(levels)
    edge = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': result, 'depth': levels, 'frontier': edge, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f207([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 208

```python
def f208(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans):
        if not result or left > result[-1][1] + max(0, gap) + 1:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    breaks = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        breaks.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': breaks, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f208([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 209

```python
def f209(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(totals) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f209([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 210

```python
def f210(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f210([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 211

```python
def f211(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y = max(-64, min(64, y + dy))
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f211([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 212

```python
def f212(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    complete = set()
    sequence = []
    groups = []
    while len(complete) < len(nodes) and len(complete) < 20:
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in complete))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f212(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 213

```python
def f213(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    complete = set()
    sequence = []
    layers = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in complete))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f213(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 214

```python
def f214(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum((max(item, 0) for item in values[pos:pos + size])))
    indexes = [pos for pos, value in enumerate(totals) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': min(256, max(totals)), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f214([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 215

```python
def f215(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    steps = {start: 0} if limit > 0 or limit < 0 else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    pending.append(nxt)
    listing = list(steps)
    furthest = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': listing, 'depth': steps, 'frontier': furthest, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f215([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 216

```python
def f216(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    rootsource = dict(needs)
    complete = set()
    sequence = []
    groups = []
    while len(complete) < len(nodes) and len(complete) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in complete))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f216(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 217

```python
def f217(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        nextmap[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    finished = set()
    result = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f217(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 218

```python
def f218(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans):
        if not result or left > result[-1][1] + gap % 5:
            result.append([left, right])
        else:
            result[-1][1] = max(0, result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f218([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 219

```python
def f219(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in repeats:
                repeats.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f219([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 220

```python
def f220(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = min(64, max(far, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f220([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 221

```python
def f221(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    terms = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f221(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 222

```python
def f222(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f222([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 223

```python
def f223(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(set(spans)):
        if not segments or left > segments[-1][1] + max(0, gap) + 1:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f223([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 224

```python
def f224(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(min(64, len(values) - size + 1)):
        series.append(sum((max(item, 0) for item in values[pos:pos + size])))
    indexes = [pos for pos, value in enumerate(series) if value >= limit]
    growth = sum((1 for pos in range(1, min(65, len(series))) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': indexes, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f224([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 225

```python
def f225(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f225(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 226

```python
def f226(board):
    board = list(board)
    known = set()
    regions = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            work = [(row, col)]
            known.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        work.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f226(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 227

```python
def f227(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    listing = []
    layers = []
    while len(complete) < len(nodes) and len(complete) < 20:
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in complete), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            complete.add(node)
            listing.append(node)
        for node in current:
            for nxt in routes[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f227(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 228

```python
def f228(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop or len(word) > 12:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    ordered = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f228(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 229

```python
def f229(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f229([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 230

```python
def f230(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    result = []
    layers = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in complete))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        layers.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f230(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 231

```python
def f231(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f231(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 232

```python
def f232(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(totals) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f232([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 233

```python
def f233(left, right, ignored):
    left = list(left)

    def normalize(value):
        return str(value).strip().upper()
    ignored = {normalize(value) for value in ignored}
    a = {normalize(value) for value in left} - ignored
    b = {normalize(value) for value in right} - ignored
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f233(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 234

```python
def f234(board):
    board = list(board)
    visited = set()
    pieces = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            pieces.append((len(cells), min(cells)))
    pieces.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in pieces], 'anchors': [list(anchor) for size, anchor in pieces], 'filled': sum((size for size, anchor in pieces)), 'count': len(pieces)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f234(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 235

```python
def f235(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        work.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f235(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 236

```python
def f236(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges[:16]:
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    lastlevel = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': lastlevel, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f236([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 237

```python
def f237(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f237(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 238

```python
def f238(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f238(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 239

```python
def f239(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(set(spans)):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = right
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f239([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 240

```python
def f240(board):
    board = list(board)
    known = set()
    pieces = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(min(len(board[row]), 10)):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            pending = [(row, col)]
            known.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        pending.append(nxt)
            pieces.append((len(cells), min(cells)))
    pieces.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in pieces], 'anchors': [list(anchor) for size, anchor in pieces], 'filled': sum((size for size, anchor in pieces)), 'count': len(pieces)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f240(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 241

```python
def f241(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \r').upper()
    excluded = {str(value).strip() for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f241(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 242

```python
def f242(left, right, ignored):
    left = list(left)

    def tidy(value):
        return str(value).strip().upper()
    ignored = {str(value).strip() for value in ignored}
    a = {tidy(value) for value in left} - ignored
    b = {tidy(value) for value in right if tidy(value) != ''} - ignored
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f242(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 243

```python
def f243(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f243([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 244

```python
def f244(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ranking = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in frequency.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ranking[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f244(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 245

```python
def f245(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    finished = set()
    sequence = []
    groups = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        groups.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f245(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 246

```python
def f246(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    handled = set()
    result = []
    layers = []
    while len(handled) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in handled), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            result.append(node)
        for node in current:
            for nxt in routes[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f246(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 247

```python
def f247(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(totals) if value >= limit and (limit >= 0 or pos > 0)]
    increases = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] >= totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f247([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 248

```python
def f248(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f248(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 249

```python
def f249(left, right, excluded):
    left = list(left)

    def canon(value):
        return str(value).strip(' ').upper()
    excluded = {str(value).upper() for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f249(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 250

```python
def f250(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    breaks = []
    for pos in range(1, min(50, len(combined))):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f250([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 251

```python
def f251(left, right, excluded):
    left = list(left)

    def canon(value):
        return str(value).strip(' \n').upper()
    excluded = {str(value).upper() for value in excluded}
    a = {canon(value) for value in left} - excluded
    b = {canon(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f251(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 252

```python
def f252(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap % 5:
            result.append([left, right])
        else:
            result[-1][1] = right
    breaks = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        breaks.append(left - result[pos - 1][1])
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': breaks, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f252([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 253

```python
def f253(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = right
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f253([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 254

```python
def f254(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    groups = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f254(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 255

```python
def f255(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            pending = [(row, col)]
            visited.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        pending.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f255(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 256

```python
def f256(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(series) if value >= limit]
    ups = sum((1 for pos in range(1, len(series)) if series[pos] >= series[pos - 1]))
    returnvalue = {'sums': series, 'best': max([0] + series), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f256([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 257

```python
def f257(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, min(50, len(result))):
        left = result[pos][0]
        gaps.append(min(100, left - result[pos - 1][1]))
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f257([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 258

```python
def f258(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(totals[:64]) if value >= limit]
    growth = sum((1 for pos in range(1, len(totals)) if totals[pos] >= totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': indexes, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f258([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 259

```python
def f259(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' ').upper()
    excluded = {str(value).upper() for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f259(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 260

```python
def f260(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ranking = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ranking[:5]], 'initials': heads, 'size': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f260(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 261

```python
def f261(left, right, banned):
    left = list(left)

    def canon(value):
        return ' '.join(str(value).split()).upper()
    banned = {str(value).upper() for value in banned}
    a = {canon(value) for value in left if canon(value) != canon(value) or canon(value) != ''} - banned
    b = {canon(value) for value in right} - banned
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f261(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 262

```python
def f262(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges:
        nextmap.setdefault(a, []).append(b)
    steps = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    work.append(nxt)
    sequence = list(steps)
    furthest = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': furthest, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f262([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 263

```python
def f263(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    sequence = list(levels)
    lastlevel = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': lastlevel[:3], 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f263([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 264

```python
def f264(board):
    board = list(board)
    known = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            queue = [(row, col)]
            known.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        if len(known) >= 100:
                            continue
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f264(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 265

```python
def f265(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges[:16]:
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(nextmap.get(cur, []))[:20]:
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    sequence = list(levels)
    edge = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': edge[:3], 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f265([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 266

```python
def f266(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(windows) if value >= limit]
    increases = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f266([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 267

```python
def f267(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f267([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 268

```python
def f268(left, right, ignored):
    left = list(left)

    def canon(value):
        return str(value).strip().upper()
    ignored = {canon(value) for value in ignored}
    a = {canon(value) for value in left} - ignored
    b = {canon(value) for value in right} - ignored
    both = a & b
    listing = sorted
    returnvalue = {'both': listing(both), 'left': listing(a - b), 'right': listing(b - a), 'all': listing(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f268(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 269

```python
def f269(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    pending.append(nxt)
    sequence = list(steps)
    edge = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': edge, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f269([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 270

```python
def f270(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f270([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 271

```python
def f271(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f271([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 272

```python
def f272(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap % 5 + 1:
            combined.append([left, right])
        else:
            combined[-1][1] = right
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f272([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 273

```python
def f273(board):
    board = list(board)
    found = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[0])):
            if col >= 12 or board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f273(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 274

```python
def f274(left, right, banned):
    left = list(left)

    def normalize(value):
        return ' '.join(str(value).split()).upper()
    banned = {normalize(value) for value in banned}
    a = {normalize(value) for value in left} - banned
    b = {normalize(value) for value in right} - banned
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f274(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 275

```python
def f275(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if needs[node] == 0 and node not in finished))
        if not available:
            break
        current = available[:1] if any((str(node).isupper() for node in nodes)) else available
        layers.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f275(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 276

```python
def f276(board):
    board = list(board)
    found = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if col >= 12 or board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f276(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 277

```python
def f277(board):
    board = list(board)
    known = set()
    regions = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in known:
                continue
            cells = []
            pending = [(row, col)]
            known.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in known):
                        known.add(nxt)
                        pending.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f277(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 278

```python
def f278(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(totals[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f278([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 279

```python
def f279(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f279([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 280

```python
def f280(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(totals) if value >= limit]
    growth = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f280([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 281

```python
def f281(left, right, ignored):
    left = list(left)

    def tidy(value):
        return str(value).strip(' \n').upper()
    ignored = {str(value).upper() for value in ignored}
    a = {tidy(value) for value in left} - ignored
    b = {tidy(value) for value in right if tidy(value) != ''} - ignored
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f281(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['GARNET'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","EMBER","FROST","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["EMBER","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 282

```python
def f282(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    crossings = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves[:20]:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in crossings:
                crossings.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f282([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 283

```python
def f283(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    sorteditems = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in tallies.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in sorteditems[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f283(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 284

```python
def f284(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f284(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 285

```python
def f285(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0} if any((start in edge for edge in edges)) else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    listing = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': listing, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f285([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 286

```python
def f286(left, right, banned):
    left = list(left)

    def normalize(value):
        return str(value).strip(' ').upper()
    banned = {normalize(value) for value in banned}
    a = {normalize(value) for value in left} - banned
    b = {normalize(value) for value in right} - banned
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((min(len(value), 8) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f286(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 287

```python
def f287(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip(' \r').upper()
    excluded = {normalize(value) for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    result = sorted
    returnvalue = {'both': result(both), 'left': result(a - b), 'right': result(b - a), 'all': result(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f287(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 288

```python
def f288(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(min(64, len(values) - size + 1)):
        series.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(series))) if series[pos] >= series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f288([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### 289

```python
def f289(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    sequence = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f289([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'C', 3)
```

```
{"count":3,"depth":{"C":0,"F":1,"H":2},"frontier":["H"],"order":["C","F","H"]}
```

### 290

```python
def f290(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    needs = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    complete = set()
    listing = []
    rounds = []
    while len(complete) < len(nodes) and len(complete) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in complete))
        if not nextbatch:
            break
        current = nextbatch
        rounds.append(current)
        for node in current:
            complete.add(node)
            listing.append(node)
        for node in current:
            for nxt in routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': listing, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f290(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 291

```python
def f291(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = right
    gaps = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f291([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 292

```python
def f292(board):
    board = list(board)
    visited = set()
    components = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            queue = [(row, col)]
            visited.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f292(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 293

```python
def f293(board):
    board = list(board)
    visited = set()
    pieces = []
    for row in range(len(board)):
        for col in range(min(len(board[row]), 10)):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            work = [(row, col)]
            visited.add((row, col))
            while work:
                cur = work.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        work.append(nxt)
            pieces.append((len(cells), min(cells)))
    pieces.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in pieces], 'anchors': [list(anchor) for size, anchor in pieces], 'filled': sum((size for size, anchor in pieces)), 'count': len(pieces)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f293(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 294

```python
def f294(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap + 1:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    gaps = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f294([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 295

```python
def f295(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = min(9, frequency.get(word, 0) + 1)
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f295(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 296

```python
def f296(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f296(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 297

```python
def f297(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f297(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 298

```python
def f298(board):
    board = list(board)
    found = set()
    components = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            queue = [(row, col)]
            found.add((row, col))
            while queue:
                cur = queue.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        queue.append(nxt)
            components.append((len(cells), min(cells)))
    components.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in components], 'anchors': [list(anchor) for size, anchor in components], 'filled': sum((size for size, anchor in components)), 'count': len(components)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f298(['..##..', '...##.', '....##', '.#....', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[4,4],[5,5]],"count":4,"filled":13,"sizes":[6,5,1,1]}
```

### 299

```python
def f299(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f299(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 300

```python
def f300(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = min(9, wordmap.get(word, 0) + 1)
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': min(256, sum((len(word) * count for word, count in wordmap.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f300(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 301

```python
def f301(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f301([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 302

```python
def f302(board):
    board = list(board)
    visited = set()
    regions = []
    for row in range(min(len(board), 10 + (len(board) - len(board)))):
        for col in range(len(board[row])):
            if board[row][col] != '#' or (row, col) in visited:
                continue
            cells = []
            pending = [(row, col)]
            visited.add((row, col))
            while pending:
                cur = pending.pop()
                cells.append(cur)
                for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
                    nxt = (cur[0] + dr, cur[1] + dc)
                    if 0 <= nxt[0] < len(board) and 0 <= nxt[1] < len(board[nxt[0]]) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in visited):
                        visited.add(nxt)
                        if len(visited) >= 100:
                            continue
                        pending.append(nxt)
            regions.append((len(cells), min(cells)))
    regions.sort(key=lambda item: (-item[0], item[1]))
    returnvalue = {'sizes': [size for size, anchor in regions], 'anchors': [list(anchor) for size, anchor in regions], 'filled': sum((size for size, anchor in regions)), 'count': len(regions)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f302(['..##..', '...##.', '...###', '.#..#.', '##..#.', '##...#'])
```

```
{"anchors":[[0,2],[3,1],[5,5]],"count":3,"filled":15,"sizes":[9,5,1]}
```

### 303

```python
def f303(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    handled = set()
    sequence = []
    rounds = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in handled))
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f303(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth')])
```

```
{"batches":[["cache","db"],["auth","jobs"],["api","proxy","worker"],["ui"]],"count":8,"order":["cache","db","auth","jobs","api","proxy","worker","ui"],"roots":["cache","db"]}
```

### 304

```python
def f304(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans):
        if not segments or left > segments[-1][1] + gap + 1:
            segments.append([left, right])
        else:
            segments[-1][1] = max(0, segments[-1][1], right)
    breaks = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        breaks.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': breaks, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f304([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 305

```python
def f305(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': min(256, sum((len(word) * count for word, count in wordmap.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f305(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 306

```python
def f306(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans, key=lambda pair: (pair[1], pair[0])):
        if not segments or left > segments[-1][1] + min(gap, 2):
            segments.append([left, right])
        else:
            segments[-1][1] = right
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f306([(3, 5), (8, 12), (15, 20), (19, 24), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":37,"holes":[3,3,5,8,7],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,53],[60,66]]}
```

### 307

```python
def f307(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    work.append(nxt)
    listing = list(distance)
    edge = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': edge, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f307([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'H', 3)
```

```
{"count":1,"depth":{"H":0},"frontier":["H"],"order":["H"]}
```

### 308

```python
def f308(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f308(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['delta'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"frost":6,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"f":6,"g":4,"h":4},"size":149,"top":["amber","cyan","frost","garnet","helium"]}
```

### 309

```python
def f309(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f309([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 310

```python
def f310(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap + 1:
            combined.append([left, right])
        else:
            combined[-1][1] = right
    breaks = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        breaks.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': breaks, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f310([(3, 5), (6, 10), (15, 20), (20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)], 2)
```

```
{"cover":39,"holes":[5,4,8,7],"longest":10,"segments":[[3,10],[15,25],[29,36],[44,53],[60,66]]}
```

### 311

```python
def f311(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    finished = set()
    listing = []
    rounds = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        rounds.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f311(['ui', 'db', 'worker', 'api', 'proxy', 'auth', 'cache', 'jobs'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache')])
```

```
{"batches":[["auth","db"],["cache","jobs","proxy"],["api","worker"],["ui"]],"count":8,"order":["auth","db","cache","jobs","proxy","api","worker","ui"],"roots":["auth","db"]}
```

### 312

```python
def f312(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, len(values) - size + 1)):
        totals.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(totals) if value >= limit]
    ups = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': min(256, max(totals)), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f312([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 313

```python
def f313(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f313([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-6,-2,2,3],"end":[-4,3],"far":8,"revisits":[[0,0],[1,0],[-1,0],[-6,-1],[-6,0]],"steps":29}
```

### 314

```python
def f314(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f314(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 315

```python
def f315(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max([0] + series), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f315([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 316

```python
def f316(left, right, excluded):
    left = list(left)

    def normalize(value):
        return str(value).strip().upper()
    excluded = {str(value).upper() for value in excluded}
    a = {normalize(value) for value in left} - excluded
    b = {normalize(value) for value in right} - excluded
    both = a & b
    sequence = sorted
    returnvalue = {'both': sequence(both), 'left': sequence(a - b), 'right': sequence(b - a), 'all': sequence(a | b), 'score': sum((len(value) for value in both))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f316(['delta', ' Amber', 'BLUE', 'ivory', 'Ember', 'GARNET', 'cyan '], [' Amber', 'delta', 'BLUE', 'helium', 'frost', 'cyan ', 'cyan '], ['Ember'])
```

```
{"all":["AMBER","BLUE","CYAN","DELTA","FROST","GARNET","HELIUM","IVORY"],"both":["AMBER","BLUE","CYAN","DELTA"],"left":["GARNET","IVORY"],"right":["FROST","HELIUM"],"score":18}
```

### 317

```python
def f317(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop or len(word) < 2:
            continue
        tallies[word] = min(9, tallies.get(word, 0) + 1)
    ordered = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f317(['Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost', 'Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'], ['frost'])
```

```
{"counts":{"amber":7,"blue":3,"cyan":6,"delta":1,"garnet":4,"helium":4},"initials":{"a":7,"b":3,"c":6,"d":1,"g":4,"h":4},"size":124,"top":["amber","cyan","garnet","helium","blue"]}
```

### 318

```python
def f318(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    repeats = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in found and list(point) not in repeats:
                repeats.append(list(point))
            found.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f318([('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2), ('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2)])
```

```
{"bounds":[-7,-2,2,3],"end":[-5,3],"far":9,"revisits":[[0,0],[1,0],[-1,0],[-7,-1],[-7,0]],"steps":30}
```

### 319

```python
def f319(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(totals[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f319([20, 21, 15, 18, 10, 7, 5, 10, 17, 14, 18, 4, 21, 22, 24], 3, 47)
```

```
{"best":67,"hits":[0,1,8,11,12],"rises":6,"sums":[56,54,43,35,22,22,32,41,49,36,43,47,67]}
```

### 320

```python
def f320(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(series) if value >= limit and (limit >= 0 or pos > 0)]
    ups = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f320([20, 21, 15, 18, 7, 7, 5, 10, 17, 14, 18, 4, 21, 24, 24], 3, 41)
```

```
{"best":69,"hits":[0,1,7,8,10,11,12],"rises":7,"sums":[56,54,40,32,19,22,32,41,49,36,43,49,69]}
```

### Final Query

Give me the output of the final query without executing it!

```python
import json, re
from collections import deque
out = {}
spans = list(((3, 5), (6, 10), (15, 20)) + ((20, 25), (29, 33), (34, 36), (44, 47), (49, 53), (60, 66)))
gap = 2
spans.sort(key=lambda pair: (pair[0], pair[1]))
parts = []
pos = 0
while pos < len(spans):
    left, right = spans[pos]
    pos += 1
    while pos < len(spans) and spans[pos][0] <= right + gap:
        right = max(right, spans[pos][1])
        pos += 1
    parts.append([left, right])
holes = [parts[pos][0] - parts[pos - 1][1] for pos in range(1, len(parts))]
record = {'aa': parts, 'bb': holes, 'cc': sum((part[1] - part[0] for part in parts)), 'dd': max((part[1] - part[0] for part in parts))}
ticket = record['cc']
left = list(('delta', ' Amber', 'BLUE', 'ivory') + ('Ember', 'GARNET', 'cyan '))
right = list((' Amber', 'delta', 'BLUE', 'helium') + ('frost', 'cyan ', 'cyan '))
route = ticket
cases = {
    37: ['GARNET'],
    39: ['Ember'],
}
blocked = cases[route]
a = set()
b = set()
ban = set()
for value in blocked:
    ban.add(value.strip().upper())
for value in left:
    value = value.strip().upper()
    if value not in ban:
        a.add(value)
for value in right:
    value = value.strip().upper()
    if value not in ban:
        b.add(value)
both = a.intersection(b)
record = {'aa': sorted(both), 'bb': sorted(a.difference(b)), 'cc': sorted(b.difference(a)), 'dd': sorted(a.union(b)), 'ee': sum(map(len, both))}
badge = record['bb'][0]
route = ticket
cases = {
    39: list((('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2)) + (('W', 1), ('W', 1), ('W', 2), ('W', 3), ('S', 2), ('N', 3), ('E', 2), ('N', 2))),
    37: list((('E', 1), ('W', 1), ('N', 2), ('E', 2), ('S', 2), ('W', 3), ('E', 2)) + (('W', 1), ('W', 4), ('W', 2), ('W', 1), ('S', 2), ('N', 3), ('E', 2), ('N', 2))),
}
moves = cases[route]
delta = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
points = [[0, 0]]
for direction, count in moves:
    dx, dy = delta[direction]
    for turn in range(count):
        points.append([points[-1][0] + dx, points[-1][1] + dy])
seen = set()
revisits = []
for point in points:
    key = tuple(point)
    if key in seen and point not in revisits:
        revisits.append(point)
    seen.add(key)
record = {'aa': points[-1], 'bb': max((abs(point[0]) + abs(point[1]) for point in points)), 'cc': revisits[:5], 'dd': [min((point[0] for point in points)), min((point[1] for point in points)), max((point[0] for point in points)), max((point[1] for point in points))], 'ee': len(points) - 1}
permit = record['bb']
nodes = list(('ui', 'db', 'worker') + ('api', 'proxy', 'auth', 'cache', 'jobs'))
options = {
    39: ('near', badge),
    37: ('far', permit),
}
route = options[ticket]
cases = {
    ('near', 'GARNET'): list((('auth', 'api'), ('db', 'api'), ('cache', 'api')) + (('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('cache', 'auth'))),
    ('near', 'EMBER'): list((('auth', 'api'), ('db', 'api'), ('cache', 'api')) + (('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache'))),
    ('far', 8): list((('auth', 'api'), ('db', 'api'), ('cache', 'api')) + (('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache'))),
    ('far', 9): list((('auth', 'api'), ('db', 'api'), ('cache', 'api')) + (('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('auth', 'cache'))),
}
edges = cases[route]
remaining = set(nodes)
done = set()
order = []
batches = []
while remaining:
    ready = sorted((node for node in remaining if all((before in done for before, after in edges if after == node))))
    if not ready:
        break
    batches.append(ready)
    order.extend(ready)
    done.update(ready)
    remaining.difference_update(ready)
roots = sorted((node for node in nodes if all((after != node for before, after in edges))))
record = {'aa': order, 'bb': batches, 'cc': roots, 'dd': len(order)}
signal = record['aa'][0]
route = permit
cases = {
    8: list(('..##..', '...##.', '....##', '.#....') + ('##..#.', '##...#')),
    9: list(('..##..', '...##.', '...###', '.#..#.') + ('##..#.', '##...#')),
}
board = cases[route]
cells = [(row, col) for row in range(len(board)) for col in range(len(board[row])) if board[row][col] == '#']
parent = {cell: cell for cell in cells}

def root(cell):
    while parent[cell] != cell:
        parent[cell] = parent[parent[cell]]
        cell = parent[cell]
    return cell

def merge(a, b):
    a = root(a)
    b = root(b)
    if a != b:
        parent[b] = a
for row, col in cells:
    for other in ((row - 1, col), (row, col - 1)):
        if other in parent:
            merge((row, col), other)
groups = {}
for cell in cells:
    groups.setdefault(root(cell), []).append(cell)
parts = [(len(group), min(group)) for group in groups.values()]
parts.sort(key=lambda item: (-item[0], item[1]))
record = {'aa': [part[0] for part in parts], 'bb': [list(part[1]) for part in parts], 'cc': len(cells), 'dd': len(parts)}
token = record['cc']
width = 3
route = (signal, token)
cases = {
    ('auth', 15): (list((20, 21, 15, 18, 7, 7, 5) + (10, 17, 14, 18, 4, 21, 24, 24)), 41),
    ('auth', 13): (list((20, 21, 15, 18, 7, 7, 5) + (10, 17, 14, 18, 4, 21, 24, 24)), 41),
    ('cache', 15): (list((20, 21, 15, 18, 7, 7, 5) + (10, 17, 14, 18, 4, 21, 24, 24)), 41),
    ('cache', 13): (list((20, 21, 15, 18, 10, 7, 5) + (10, 17, 14, 18, 4, 21, 22, 24)), 47),
}
values, limit = cases[route]
current = sum(values[:width])
sums = [current]
for pos in range(width, len(values)):
    current += values[pos] - values[pos - width]
    sums.append(current)
hits = []
rises = 0
for pos, value in enumerate(sums):
    if value >= limit:
        hits.append(pos)
    if pos and value > sums[pos - 1]:
        rises += 1
record = {'aa': hits, 'bb': max(sums), 'cc': rises, 'dd': sums}
memo = record['bb']
lines = list(('Frost, frost. amber helium', 'Helium, cyan. cyan garnet frost') + ('Cyan, helium. amber delta', 'Helium, blue. frost garnet garnet', 'Cyan, amber. frost blue', 'Amber, amber. garnet amber blue', 'Amber, cyan. frost cyan'))
route = memo
cases = {
    67: ['delta'],
    69: ['frost'],
}
stop = cases[route]
normalized = set()
for item in stop:
    normalized.add(item.lower())
stop = normalized
words = []
for line in lines:
    words.extend(re.findall('[a-z]+', line.lower()))
words = [word for word in words if word not in stop]
counts = {}
initials = {}
for word in words:
    counts[word] = counts.get(word, 0) + 1
    initials[word[0]] = initials.get(word[0], 0) + 1
top = sorted(counts, key=lambda word: (-counts[word], word))[:5]
record = {'aa': top, 'bb': counts, 'cc': initials, 'dd': sum((len(word) for word in words))}
clue = record['dd']
edges = list((('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F')) + (('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')))
limit = 3
route = clue
cases = {
    124: 'C',
    149: 'H',
}
start = cases[route]
links = {}
for edge in edges:
    links.setdefault(edge[0], []).append(edge[1])
distance = {start: 0}
queue = deque([start])
while queue:
    node = queue.popleft()
    if distance[node] == limit:
        continue
    for child in sorted(links.get(node, [])):
        if child in distance:
            continue
        distance[child] = distance[node] + 1
        queue.append(child)
furthest = max(distance.values())
record = {'aa': list(distance), 'bb': distance, 'cc': sorted((node for node in distance if distance[node] == furthest)), 'dd': len(distance)}
out['aa'] = record['aa']
out['bb'] = record['bb']
out['cc'] = record['cc']
out['dd'] = record['dd']
print(json.dumps(out, separators=(",", ":"), sort_keys=True))
```