tasks/program-execution-tracing/contexts/sample-00003.md

### 001

```python
def f1(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap and rate0 != 0:
            ratemap[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in ratemap and count > 0:
            matched.append((key, count * ratemap[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': leftover, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f1([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 002

```python
def f2(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 sorted(children.get(cur, []))[:20]:
                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, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f2([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 003

```python
def f3(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
    initial = dict(indegree)
    handled = set()
    sequence = []
    rounds = []
    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
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                indegree[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
```

Example call:

```
f3(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 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)}
    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, 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
```

Example call:

```
f4([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 005

```python
def f5(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}
    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)
    complete = set()
    result = []
    rounds = []
    while len(complete) < len(nodes):
        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)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[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
```

Example call:

```
f5(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 006

```python
def f6(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
```

Example call:

```
f6([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 007

```python
def f7(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in prices and count > 0:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': leftover, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f7([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 008

```python
def f8(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[: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(series), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f8([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 009

```python
def f9(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()
    result = []
    layers = []
    while len(handled) < len(nodes):
        nextbatch = 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 nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        layers.append(current)
        for node in current:
            handled.add(node)
            result.append(node)
        for node in current:
            for nxt in children[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
```

Example call:

```
f9(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 010

```python
def f10(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
    rootsource = dict(incoming)
    complete = set()
    sequence = []
    groups = []
    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), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        groups.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': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f10(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 011

```python
def f11(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        if name0 not in ratemap or rate0 <= rate0 + 0:
            ratemap[name0] = rate0
    items = []
    for key, count in left:
        if key in ratemap and count > 0:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f11([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 012

```python
def f12(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] = 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
```

Example call:

```
f12([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 013

```python
def f13(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':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = min(9, 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
```

Example call:

```
f13(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 014

```python
def f14(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 and (limit >= 0 or pos > 0)]
    ups = 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': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f14([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 015

```python
def f15(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[:64]:
        if word in stop or len(word) < 2:
            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
```

Example call:

```
f15(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 016

```python
def f16(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted((pair for pair in spans if pair[0] <= pair[1])):
        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)
    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
```

Example call:

```
f16([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 017

```python
def f17(nodes, edges):
    nodes = list(nodes)
    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
    startdegree = dict(incoming)
    finished = set()
    result = []
    layers = []
    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
        layers.append(current)
        for node in current:
            finished.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 startdegree[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

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

### 018

```python
def f18(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 = []
    layers = []
    while len(finished) < len(nodes):
        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)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

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

### 019

```python
def f19(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices or rate0 <= rate0 + 0:
            prices[name0] = rate0
    matched = []
    for key, count in left:
        if key in prices:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f19([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 020

```python
def f20(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 board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            pending = [(row, col)]
            found.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 found):
                        found.add(nxt)
                        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
```

Example call:

```
f20(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 021

```python
def f21(board):
    board = list(board)
    found = 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 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 (nxt[1] < 12) and (board[nxt[0]][nxt[1]] == '#') and (nxt not in found):
                        found.add(nxt)
                        if len(found) >= 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
```

Example call:

```
f21(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 022

```python
def f22(nodes, edges):
    nodes = list(nodes)
    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()
    result = []
    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), reverse=len(nodes) > 20)
        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]:
                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
```

Example call:

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

Output example:

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

### 023

```python
def f23(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices and rate0 != 0:
            prices[name0] = rate0
    combined = []
    for key, count in left:
        if key in prices:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f23([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 024

```python
def f24(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:
        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
```

Example call:

```
f24([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 025

```python
def f25(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
    ordered = 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 ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f25(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 026

```python
def f26(lines, stop):
    lines = list(lines)
    frequency = {}
    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 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
```

Example call:

```
f26(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 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)}
    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 = max(-64, min(64, 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 = (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
```

Example call:

```
f27([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 028

```python
def f28(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
```

Example call:

```
f28([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 029

```python
def f29(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)
                        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
```

Example call:

```
f29(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 030

```python
def f30(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges:
        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 (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                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, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f30([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 031

```python
def f31(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
```

Example call:

```
f31([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 032

```python
def f32(board):
    board = list(board)
    visited = set()
    regions = []
    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)
                        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
```

Example call:

```
f32(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 033

```python
def f33(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors:
            factors[name0] = rate0
    matched = []
    for key, count in left:
        if key in factors:
            matched.append((key, count * factors[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f33([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 034

```python
def f34(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}
    pending = [start]
    while pending:
        cur = pending.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
                    pending.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
```

Example call:

```
f34([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 035

```python
def f35(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 = []
            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)
            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
```

Example call:

```
f35(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 036

```python
def f36(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
```

Example call:

```
f36(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 037

```python
def f37(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    indexes = [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': indexes, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f37([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 038

```python
def f38(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':
                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
```

Example call:

```
f38(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 039

```python
def f39(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left:
        if key in prices:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len({key for key, value in combined})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f39([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 040

```python
def f40(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 (node for node in sorted(routes.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    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
```

Example call:

```
f40([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 041

```python
def f41(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors:
            factors[name0] = rate0
    items = []
    for key, count in left[:20]:
        if key in factors:
            items.append((key, count * factors[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len({key for key, value in items})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f41([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 042

```python
def f42(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 = 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': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f42([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 043

```python
def f43(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 = []
            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
```

Example call:

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

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 044

```python
def f44(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 board[row][col] != '#' or (row, col) in found:
                continue
            cells = []
            pending = [(row, col)]
            found.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 found):
                        found.add(nxt)
                        if len(found) >= 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
```

Example call:

```
f44(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 045

```python
def f45(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] < 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
                    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, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 046

```python
def f46(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, 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
```

Example call:

```
f46([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 047

```python
def f47(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)
    complete = set()
    result = []
    groups = []
    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
        groups.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': result, 'batches': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f47(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 048

```python
def f48(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.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(children.get(cur, []))[:20]:
                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
```

Example call:

```
f48([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 049

```python
def f49(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 (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                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, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f49([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 050

```python
def f50(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]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f50([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 051

```python
def f51(nodes, edges):
    nodes = list(nodes)
    needs = {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)
        needs[b] += 1
    rootsource = dict(needs)
    finished = set()
    sequence = []
    rounds = []
    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))
        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 routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f51(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 052

```python
def f52(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
```

Example call:

```
f52([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 053

```python
def f53(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}
    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)
    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
```

Example call:

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

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 054

```python
def f54(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in prices:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f54([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 055

```python
def f55(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
    initial = dict(indegree)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = 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 nextbatch:
            break
        current = nextbatch
        layers.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': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f55(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 056

```python
def f56(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices:
            prices[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in prices:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f56([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 057

```python
def f57(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices:
            prices[name0] = rate0
    items = []
    for key, count in left:
        if key in prices:
            items.append((key, count * prices[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f57([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 058

```python
def f58(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:
        if word in stop:
            continue
        tallies[word] = min(9, 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': min(256, sum((len(word) * count for word, count in tallies.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f58(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 059

```python
def f59(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(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 = (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
```

Example call:

```
f59([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 060

```python
def f60(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]
    growth = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f60([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 061

```python
def f61(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]))
    positions = [pos for pos, value in enumerate(series) if value > limit]
    growth = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': min(256, max(series)), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f61([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 062

```python
def f62(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
    initial = dict(indegree)
    finished = set()
    sequence = []
    rounds = []
    while len(finished) < len(nodes):
        nextbatch = 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 nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        rounds.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': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f62(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 063

```python
def f63(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:
        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 crossings:
                crossings.append(list(point))
            found.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
```

Example call:

```
f63([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 064

```python
def f64(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}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(routes.get(cur, []))[:20]:
                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
```

Example call:

```
f64([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 065

```python
def f65(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 = 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
```

Example call:

```
f65([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 066

```python
def f66(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
    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))
        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 nextmap[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
```

Example call:

```
f66(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 067

```python
def f67(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 = []
            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)
            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
```

Example call:

```
f67(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 068

```python
def f68(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        if name0 not in ratemap and rate0 != 0:
            ratemap[name0] = rate0
    items = []
    for key, count in left:
        if key in ratemap and count > 0:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': leftover, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f68([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 069

```python
def f69(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(min(64, 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, min(65, 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
```

Example call:

```
f69([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 070

```python
def f70(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]
    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': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f70([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 071

```python
def f71(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.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(children.get(cur, [])):
                if nxt not in distance:
                    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
```

Example call:

```
f71([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 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)}
    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, 64)):
            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
```

Example call:

```
f72([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 073

```python
def f73(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices:
            prices[name0] = rate0
    matched = []
    for key, count in left:
        if key in prices and count > 0:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f73([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 074

```python
def f74(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 % 5:
            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
```

Example call:

```
f74([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 075

```python
def f75(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors:
            factors[name0] = rate0
    matched = []
    for key, count in left:
        if key in factors and count > 0:
            matched.append((key, count * factors[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': leftover, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f75([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 076

```python
def f76(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)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[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
        layers.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in nextmap[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
```

Example call:

```
f76(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 077

```python
def f77(board):
    board = list(board)
    visited = set()
    pieces = []
    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)
            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
```

Example call:

```
f77(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 078

```python
def f78(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices or rate0 <= rate0 + 0:
            prices[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in prices:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f78([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 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
```

Example call:

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

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 080

```python
def f80(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans):
        if not segments or left > segments[-1][1] + gap:
            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((min(100, 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
```

Example call:

```
f80([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 081

```python
def f81(lines, stop):
    lines = list(lines)
    tallies = {}
    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
        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
```

Example call:

```
f81(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 082

```python
def f82(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:
        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 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
```

Example call:

```
f82([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 083

```python
def f83(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[: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
        tallies[word] = tallies.get(word, 0) + 1
    sorteditems = 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 sorteditems[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f83(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 084

```python
def f84(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:
            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
```

Example call:

```
f84(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 085

```python
def f85(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' 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) > 12:
            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
```

Example call:

```
f85(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 086

```python
def f86(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors or rate0 <= rate0 + 0:
            factors[name0] = rate0
    combined = []
    for key, count in left:
        if key in factors:
            combined.append((key, count * factors[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f86([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 087

```python
def f87(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
    initial = dict(indegree)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in handled), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[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
```

Example call:

```
f87(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 088

```python
def f88(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[:64]) if value >= limit]
    growth = 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': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f88([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 089

```python
def f89(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors:
            factors[name0] = rate0
    items = []
    for key, count in left:
        if key in factors:
            items.append((key, count * factors[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in factors})
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f89([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 090

```python
def f90(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left:
        if key in prices and count > 0:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f90([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 091

```python
def f91(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 = 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 = 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': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f91([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 092

```python
def f92(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(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, 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
```

Example call:

```
f92([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 093

```python
def f93(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:
        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
```

Example call:

```
f93(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 094

```python
def f94(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]
    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
```

Example call:

```
f94([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 095

```python
def f95(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() 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[: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
```

Example call:

```
f95(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 096

```python
def f96(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) 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]))
    heads = {}
    for word, count in wordmap.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f96(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 097

```python
def f97(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)
    handled = set()
    sequence = []
    rounds = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in handled), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[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
```

Example call:

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

Output example:

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

### 098

```python
def f98(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 = []
    groups = []
    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), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        groups.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': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f98(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 099

```python
def f99(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 = []
    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 initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

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

### 100

```python
def f100(board):
    board = list(board)
    found = set()
    pieces = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            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)
            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
```

Example call:

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

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 101

```python
def f101(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in prices and count > 0:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f101([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 102

```python
def f102(lines, stop):
    lines = list(lines)
    tallies = {}
    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 or len(word) > 12:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    ranking = 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 ranking[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f102(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 103

```python
def f103(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors:
            factors[name0] = rate0
    combined = []
    for key, count in left:
        if key in factors:
            combined.append((key, count * factors[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len({key for key, value in combined})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f103([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 104

```python
def f104(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)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in levels and (not nxt.startswith('Z')):
                    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
```

Example call:

```
f104([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 105

```python
def f105(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[:64]:
        if word in stop:
            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
```

Example call:

```
f105(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 106

```python
def f106(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
    startdegree = dict(indegree)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = 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 nextbatch:
            break
        current = nextbatch
        layers.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': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f106(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 107

```python
def f107(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
    startdegree = dict(needs)
    complete = set()
    result = []
    groups = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if needs[node] == 0 and node not in complete), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        groups.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': result, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f107(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 108

```python
def f108(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]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f108([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 109

```python
def f109(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 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)
            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
```

Example call:

```
f109(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 110

```python
def f110(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(0, 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
```

Example call:

```
f110([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 111

```python
def f111(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 = 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 = 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
```

Example call:

```
f111([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 112

```python
def f112(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 = 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 crossings:
                crossings.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': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f112([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 113

```python
def f113(nodes, edges):
    nodes = list(nodes)
    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
    initial = dict(indegree)
    finished = set()
    sequence = []
    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), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                indegree[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
```

Example call:

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

Output example:

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

### 114

```python
def f114(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges:
        nextmap.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 sorted(nextmap.get(cur, []))[:20]:
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    queue.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
```

Example call:

```
f114([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 115

```python
def f115(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)
    finished = set()
    result = []
    groups = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished))
        if not available:
            break
        current = available
        groups.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': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f115(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 116

```python
def f116(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[: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 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
```

Example call:

```
f116([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 117

```python
def f117(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 % 100):
            x = max(-64, min(64, 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 = (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
```

Example call:

```
f117([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 118

```python
def f118(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, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': min(256, max(windows)), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f118([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 119

```python
def f119(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)
    handled = set()
    sequence = []
    rounds = []
    while len(handled) < len(nodes) and len(handled) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in handled))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        rounds.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

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

### 120

```python
def f120(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 = min(64, 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, 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
```

Example call:

```
f120([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 121

```python
def f121(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    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)
    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
```

Example call:

```
f121([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 122

```python
def f122(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans, key=lambda pair: pair[0]):
        if not combined or left > combined[-1][1] + gap % 5 + 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
```

Example call:

```
f122([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 123

```python
def f123(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((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
```

Example call:

```
f123([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 124

```python
def f124(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(set(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
```

Example call:

```
f124([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 125

```python
def f125(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()
    result = []
    rounds = []
    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))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        rounds.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                needs[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
```

Example call:

```
f125(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 126

```python
def f126(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 = []
            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
```

Example call:

```
f126(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 127

```python
def f127(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
    initial = dict(incoming)
    finished = set()
    result = []
    layers = []
    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))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.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
```

Example call:

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

Output example:

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

### 128

```python
def f128(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)
    finished = set()
    sequence = []
    layers = []
    while len(finished) < len(nodes):
        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
        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 initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f128(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 129

```python
def f129(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
    startdegree = dict(incoming)
    finished = set()
    result = []
    layers = []
    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
        layers.append(current)
        for node in current:
            finished.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 startdegree[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f129(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 130

```python
def f130(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:
            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) > 12:
            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': min(256, sum((len(word) * count for word, count in tallies.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f130(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 131

```python
def f131(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) 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:
        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
```

Example call:

```
f131(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 132

```python
def f132(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]
    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
```

Example call:

```
f132([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 133

```python
def f133(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
    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
```

Example call:

```
f133([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 134

```python
def f134(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:
            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
```

Example call:

```
f134(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 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 = []
            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)
            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
```

Example call:

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

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 136

```python
def f136(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 += 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 = (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
```

Example call:

```
f136([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 137

```python
def f137(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] + gap % 5:
            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': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f137([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 138

```python
def f138(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + max(0, gap) + 1:
            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
```

Example call:

```
f138([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 139

```python
def f139(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] < limit:
            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
```

Example call:

```
f139([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 140

```python
def f140(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)
    result = list(distance)
    lastlevel = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': lastlevel[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f140([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 141

```python
def f141(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted((pair for pair in spans if pair[0] <= pair[1])):
        if not segments or left > segments[-1][1] + gap:
            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
```

Example call:

```
f141([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 142

```python
def f142(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)
    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(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    work.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
```

Example call:

```
f142([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 143

```python
def f143(lines, stop):
    lines = list(lines)
    frequency = {}
    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
        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': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f143(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 144

```python
def f144(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges:
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0} if any((start in edge for edge in edges)) else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    pending.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
```

Example call:

```
f144([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 145

```python
def f145(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(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
```

Example call:

```
f145([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 146

```python
def f146(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 = 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': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f146([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 147

```python
def f147(board):
    board = list(board)
    known = set()
    regions = []
    for row in range(len(board)):
        for col in range(len(board[0])):
            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)
            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
```

Example call:

```
f147(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 148

```python
def f148(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[:20]:
        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 known and list(point) not in crossings:
                crossings.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': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f148([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 149

```python
def f149(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    items = []
    for key, count in left[:20]:
        if key in prices:
            items.append((key, count * prices[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f149([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 150

```python
def f150(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[: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] = 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
```

Example call:

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

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 151

```python
def f151(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, 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
```

Example call:

```
f151([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 152

```python
def f152(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 += 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
```

Example call:

```
f152([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 153

```python
def f153(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 = []
            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)
                        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
```

Example call:

```
f153(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 154

```python
def f154(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
    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
```

Example call:

```
f154([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 155

```python
def f155(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)
    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
```

Example call:

```
f155([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 156

```python
def f156(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)
    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:
                    distance[nxt] = distance[cur] + 1
                    work.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
```

Example call:

```
f156([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 157

```python
def f157(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 = 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
```

Example call:

```
f157([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 158

```python
def f158(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] = 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
```

Example call:

```
f158([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 159

```python
def f159(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left:
        if key in prices and count > 0:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len({key for key, value in combined})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f159([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 160

```python
def f160(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in ratemap:
            combined.append((key, count * ratemap[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in ratemap})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f160([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 161

```python
def f161(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)
    steps = {start: 0} if limit > 0 or limit < 0 else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                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[:3], 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f161([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 162

```python
def f162(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((max(item, 0) for item in values[pos:pos + size])))
    indexes = [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': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f162([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 163

```python
def f163(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    items = []
    for key, count in left:
        if key in ratemap:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': leftover, 'count': len({key for key, value in items})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f163([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 164

```python
def f164(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[: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
```

Example call:

```
f164(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 165

```python
def f165(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 = []
            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
```

Example call:

```
f165(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 166

```python
def f166(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}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                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
```

Example call:

```
f166([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 167

```python
def f167(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
    initial = dict(needs)
    complete = set()
    result = []
    layers = []
    while len(complete) < len(nodes) and len(complete) < 20:
        available = sorted((node for node in nodes if needs[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 routes[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
```

Example call:

```
f167(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 168

```python
def f168(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 = []
            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
```

Example call:

```
f168(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 169

```python
def f169(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.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 sorted(routes.get(cur, []))[:20]:
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.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[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f169([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 170

```python
def f170(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)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    work.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
```

Example call:

```
f170([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 171

```python
def f171(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] < 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
                    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
```

Example call:

```
f171([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 172

```python
def f172(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[0])):
            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)
                        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
```

Example call:

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

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 173

```python
def f173(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 = max(-64, min(64, 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 = (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
```

Example call:

```
f173([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 174

```python
def f174(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 += 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
```

Example call:

```
f174([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 175

```python
def f175(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] = 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
```

Example call:

```
f175([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 176

```python
def f176(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, 64)):
            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
```

Example call:

```
f176([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 177

```python
def f177(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, []))[:20]:
                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
```

Example call:

```
f177([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 178

```python
def f178(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 and (limit >= 0 or pos > 0)]
    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
```

Example call:

```
f178([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 179

```python
def f179(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 = []
            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)
            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
```

Example call:

```
f179(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 180

```python
def f180(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' 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]))
    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
```

Example call:

```
f180(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 181

```python
def f181(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[: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
```

Example call:

```
f181(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 182

```python
def f182(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(set(spans)):
        if not segments or left > segments[-1][1] + gap % 5:
            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
```

Example call:

```
f182([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 183

```python
def f183(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
    initial = dict(indegree)
    finished = set()
    listing = []
    groups = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished))
        if not available:
            break
        current = available
        groups.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': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f183(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 184

```python
def f184(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[: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] = 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
```

Example call:

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

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 185

```python
def f185(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)
    steps = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    pending.append(nxt)
    result = list(steps)
    furthest = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': result, 'depth': steps, 'frontier': furthest[:3], 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f185([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 186

```python
def f186(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in prices:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len({key for key, value in combined})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f186([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 187

```python
def f187(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) 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:
        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
```

Example call:

```
f187(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 188

```python
def f188(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] + max(0, gap):
            segments.append([left, right])
        else:
            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
```

Example call:

```
f188([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 189

```python
def f189(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right[:20]:
        if name0 not in prices:
            prices[name0] = rate0
    items = []
    for key, count in left:
        if key in prices:
            items.append((key, count * prices[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in prices})
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len({key for key, value in items})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f189([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 190

```python
def f190(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors or rate0 <= rate0 + 0:
            factors[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in factors:
            matched.append((key, count * factors[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f190([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 191

```python
def f191(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices or rate0 <= rate0 + 0:
            prices[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in prices:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f191([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 192

```python
def f192(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(set(spans)):
        if not result or left > result[-1][1] + gap % 5:
            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
```

Example call:

```
f192([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 193

```python
def f193(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 = 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, 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
```

Example call:

```
f193([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 194

```python
def f194(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[:64]) if value >= limit]
    growth = 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': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f194([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 195

```python
def f195(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    items = []
    for key, count in left:
        if key in ratemap and count > 0:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted({key for key, count in left if key not in ratemap})
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': leftover, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f195([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 196

```python
def f196(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(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
```

Example call:

```
f196([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 197

```python
def f197(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 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
```

Example call:

```
f197(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 198

```python
def f198(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 = []
            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 (nxt[1] < 12) 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
```

Example call:

```
f198(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 199

```python
def f199(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)
    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
```

Example call:

```
f199([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 200

```python
def f200(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 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
```

Example call:

```
f200(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 201

```python
def f201(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    matched = []
    for key, count in left:
        if key in prices:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f201([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 202

```python
def f202(nodes, edges):
    nodes = list(nodes)
    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
    startdegree = 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 nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': rounds, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f202(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 203

```python
def f203(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges[:16]:
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.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
                    pending.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
```

Example call:

```
f203([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 204

```python
def f204(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[: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
    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
```

Example call:

```
f204(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 205

```python
def f205(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(count):
            x = max(-64, min(64, 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
```

Example call:

```
f205([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 206

```python
def f206(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:
            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
```

Example call:

```
f206(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 207

```python
def f207(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 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
```

Example call:

```
f207(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 208

```python
def f208(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)
    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': min(100, max((right - left for left, right in result)))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f208([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 209

```python
def f209(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors:
            factors[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in factors and count > 0:
            combined.append((key, count * factors[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in factors})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f209([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 210

```python
def f210(lines, stop):
    lines = list(lines)
    wordmap = {}
    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:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in wordmap.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f210(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 211

```python
def f211(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in prices:
            matched.append((key, count * prices[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f211([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 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}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in handled))
        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:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[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
```

Example call:

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

Output example:

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

### 213

```python
def f213(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
    rootsource = dict(needs)
    complete = set()
    listing = []
    groups = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in complete), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            complete.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': listing, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

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

Output example:

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

### 214

```python
def f214(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
    initial = dict(incoming)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes):
        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)
            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
```

Example call:

```
f214(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 215

```python
def f215(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
    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))
        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 nextmap[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
```

Example call:

```
f215(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 216

```python
def f216(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 = 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
```

Example call:

```
f216([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 217

```python
def f217(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    items = []
    for key, count in left:
        if key in ratemap:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted({key for key, count in left if key not in ratemap})
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': unmatched, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f217([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 218

```python
def f218(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 % 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
```

Example call:

```
f218([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 219

```python
def f219(values, width, limit):
    values = list(values)
    size = width
    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 and (limit >= 0 or pos > 0)]
    ups = sum((1 for pos in range(1, 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
```

Example call:

```
f219([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 220

```python
def f220(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors:
            factors[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in factors:
            combined.append((key, count * factors[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted({key for key, count in left if key not in factors})
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': absent, 'count': len({key for key, value in combined})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f220([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 221

```python
def f221(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
```

Example call:

```
f221([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 222

```python
def f222(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, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max([0] + totals), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f222([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 223

```python
def f223(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]
    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
```

Example call:

```
f223([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 224

```python
def f224(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
```

Example call:

```
f224([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 225

```python
def f225(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.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(children.get(cur, []))[:20]:
                if nxt not in distance and (not nxt.startswith('Z')):
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    result = list(distance)
    edge = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': edge, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f225([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 226

```python
def f226(board):
    board = list(board)
    found = set()
    pieces = []
    for row in range(len(board)):
        for col in range(len(board[row])):
            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)
            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
```

Example call:

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

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 227

```python
def f227(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, []))[:20]:
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    pending.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[:3], 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f227([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 228

```python
def f228(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + gap % 5:
            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
```

Example call:

```
f228([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 229

```python
def f229(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':
                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
```

Example call:

```
f229(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 230

```python
def f230(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}
    queue = [start]
    while queue:
        cur = queue.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
                    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
```

Example call:

```
f230([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 231

```python
def f231(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[: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
```

Example call:

```
f231(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 232

```python
def f232(nodes, edges):
    nodes = list(nodes)
    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
    initial = dict(indegree)
    finished = set()
    sequence = []
    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), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        rounds.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': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f232(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 233

```python
def f233(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(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
```

Example call:

```
f233([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 234

```python
def f234(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]))
    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([0] + series), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f234([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 235

```python
def f235(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    levels = {start: 0} if any((start in edge for edge in edges)) else {}
    pending = [start]
    while pending:
        cur = pending.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
                    pending.append(nxt)
    result = list(levels)
    lastlevel = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': result, 'depth': levels, 'frontier': lastlevel, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f235([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 236

```python
def f236(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(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, 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
```

Example call:

```
f236([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 237

```python
def f237(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans):
        if not segments or left > segments[-1][1] + max(0, gap):
            segments.append([left, right])
        else:
            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
```

Example call:

```
f237([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 238

```python
def f238(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 = []
            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
```

Example call:

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

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 239

```python
def f239(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]))
    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
```

Example call:

```
f239(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 240

```python
def f240(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(set(spans)):
        if not segments or left > segments[-1][1] + max(0, gap):
            segments.append([left, right])
        else:
            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
```

Example call:

```
f240([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 241

```python
def f241(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
```

Example call:

```
f241([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 242

```python
def f242(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' 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
        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
```

Example call:

```
f242(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 243

```python
def f243(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
    rootsource = 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 rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f243(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 244

```python
def f244(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 = []
            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 (nxt[1] < 12) 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
```

Example call:

```
f244(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 245

```python
def f245(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:
        a, b = (before, after)
        nextmap[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    finished = set()
    result = []
    layers = []
    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=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.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
```

Example call:

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

Output example:

```
{"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(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(len(values) - size + 1):
        totals.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(totals[:64]) 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': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f246([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 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]
    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': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f247([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 248

```python
def f248(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, 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
```

Example call:

```
f248([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 249

```python
def f249(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[:64]) if value >= limit and (limit >= 0 or pos > 0)]
    ups = sum((1 for pos in range(1, 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
```

Example call:

```
f249([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 250

```python
def f250(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors:
            factors[name0] = rate0
    matched = []
    for key, count in left:
        if key in factors:
            matched.append((key, count * factors[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in factors))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f250([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 251

```python
def f251(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(set(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, 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
```

Example call:

```
f251([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 252

```python
def f252(board):
    board = list(board)
    found = 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 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 (nxt[1] < 12) 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
```

Example call:

```
f252(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 253

```python
def f253(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] = min(9, tallies.get(word, 0) + 1)
    ranking = 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 ranking[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f253(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 254

```python
def f254(board):
    board = list(board)
    visited = set()
    pieces = []
    for row in range(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)
                        if len(visited) >= 100:
                            continue
                        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
```

Example call:

```
f254(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 255

```python
def f255(values, width, limit):
    values = list(values)
    size = width
    totals = []
    for pos in range(min(64, 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]
    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
```

Example call:

```
f255([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 256

```python
def f256(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 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': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f256(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 257

```python
def f257(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)
                        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
```

Example call:

```
f257(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 258

```python
def f258(values, width, limit):
    values = list(values)
    size = width
    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]
    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
```

Example call:

```
f258([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 259

```python
def f259(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] = max(0, 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
```

Example call:

```
f259([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 260

```python
def f260(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]))
    positions = [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': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f260([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 261

```python
def f261(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans):
        if not result or left > result[-1][1] + min(gap, 2):
            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
```

Example call:

```
f261([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 262

```python
def f262(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        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)
    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
```

Example call:

```
f262([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 263

```python
def f263(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 = 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 = 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': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f263([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 264

```python
def f264(board):
    board = list(board)
    known = 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 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
```

Example call:

```
f264(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 265

```python
def f265(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 % 5:
            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
```

Example call:

```
f265([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 266

```python
def f266(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans, key=lambda pair: (pair[1], pair[0])):
        if not result or left > result[-1][1] + gap % 5:
            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(min(100, 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
```

Example call:

```
f266([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 267

```python
def f267(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted((pair for pair in spans if pair[0] < pair[1] or pair[0] != pair[1])):
        if not segments or left > segments[-1][1] + gap:
            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': min(100, max((right - left for left, right in segments)))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f267([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 268

```python
def f268(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 = []
            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)
            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
```

Example call:

```
f268(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 269

```python
def f269(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    matched = []
    for key, count in left:
        if key in ratemap:
            matched.append((key, count * ratemap[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': absent, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f269([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 270

```python
def f270(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, 64)):
            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 = 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
```

Example call:

```
f270([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 271

```python
def f271(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    breaks = []
    for pos in range(1, min(50, len(segments))):
        left = segments[pos][0]
        breaks.append(min(100, 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
```

Example call:

```
f271([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 272

```python
def f272(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)
    levels = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if levels[cur] < min(limit, 3):
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in levels and (not nxt.startswith('Z')):
                    levels[nxt] = levels[cur] + 1
                    pending.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
```

Example call:

```
f272([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 273

```python
def f273(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 = 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
```

Example call:

```
f273([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 274

```python
def f274(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 = []
            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
```

Example call:

```
f274(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 275

```python
def f275(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)
    handled = set()
    sequence = []
    groups = []
    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
        groups.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': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f275(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 276

```python
def f276(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])))
    indexes = [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(windows), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f276([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 277

```python
def f277(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap and rate0 != 0:
            ratemap[name0] = rate0
    matched = []
    for key, count in left:
        if key in ratemap:
            matched.append((key, count * ratemap[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    leftover = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': leftover, 'count': len({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f277([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 278

```python
def f278(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
    rootsource = dict(incoming)
    finished = set()
    result = []
    groups = []
    while len(finished) < len(nodes):
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in finished))
        if not available:
            break
        current = available
        groups.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': result, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f278(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

Output example:

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

### 279

```python
def f279(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[: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) > 12:
            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
```

Example call:

```
f279(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 280

```python
def f280(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 and (limit >= 0 or pos > 0)]
    ups = sum((1 for pos in range(1, min(65, len(series))) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': min(256, max(series)), 'hits': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f280([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 281

```python
def f281(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(spans):
        if not result or left > result[-1][1] + gap + 1:
            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((min(100, right - left) for left, right in result)), 'holes': spaces, 'longest': min(100, max((right - left for left, right in result)))}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f281([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 282

```python
def f282(board):
    board = list(board)
    visited = set()
    pieces = []
    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)
            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
```

Example call:

```
f282(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 283

```python
def f283(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 += dx
            y = max(-64, min(64, 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 = (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
```

Example call:

```
f283([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 284

```python
def f284(lines, stop):
    lines = list(lines)
    tallies = {}
    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
        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
```

Example call:

```
f284(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 285

```python
def f285(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.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[:3], 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f285([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 286

```python
def f286(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 % 100):
            x += dx
            y = max(-64, min(64, 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, 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
```

Example call:

```
f286([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 287

```python
def f287(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.setdefault(a, []).append(b)
    steps = {start: 0} if limit > 0 or limit < 0 else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in sorted(routes.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
```

Example call:

```
f287([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 288

```python
def f288(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)
                        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
```

Example call:

```
f288(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 289

```python
def f289(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]
    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
```

Example call:

```
f289([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 290

```python
def f290(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(min(count, 64)):
            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 = (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
```

Example call:

```
f290([('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[0,-6,10,0],"end":[7,-3],"far":16,"revisits":[[4,0],[3,0],[2,0],[4,-1]],"steps":38}
```

### 291

```python
def f291(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}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                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
```

Example call:

```
f291([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 292

```python
def f292(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    items = []
    for key, count in left[:20]:
        if key in ratemap:
            items.append((key, count * ratemap[key] + fee))
    items.sort(key=lambda item: (-item[1], item[0]))
    absent = sorted((key for key, count in left if key not in ratemap))
    returnvalue = {'items': [[key, value] for key, value in items[:5]], 'total': sum((value for key, value in items)), 'missing': absent, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f292([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 293

```python
def f293(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
```

Example call:

```
f293(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 294

```python
def f294(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(set(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((min(100, 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
```

Example call:

```
f294([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 295

```python
def f295(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans, key=lambda pair: pair[0]):
        if not combined or left > combined[-1][1] + gap:
            combined.append([left, right])
        else:
            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
```

Example call:

```
f295([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 1)
```

Output example:

```
{"cover":39,"holes":[7,7,4,5],"longest":11,"segments":[[3,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 296

```python
def f296(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 % 100):
            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 = (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
```

Example call:

```
f296([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 297

```python
def f297(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}
    queue = [start]
    while queue:
        cur = queue.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
                    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
```

Example call:

```
f297([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 298

```python
def f298(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 % 100):
            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
```

Example call:

```
f298([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 299

```python
def f299(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 = []
            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
```

Example call:

```
f299(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 300

```python
def f300(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.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(routes.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.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
```

Example call:

```
f300([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 301

```python
def f301(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]
    growth = 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': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f301([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 302

```python
def f302(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()
    result = []
    groups = []
    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=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        groups.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in routes[node]:
                needs[nxt] -= 1
    returnvalue = {'order': result, 'batches': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f302(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 303

```python
def f303(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]
    growth = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f303([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### 304

```python
def f304(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in edges:
        routes.setdefault(a, []).append(b)
    steps = {start: 0} if any((start in edge for edge in edges)) else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(routes.get(cur, []))[:20]:
                if nxt not in steps and (not nxt.startswith('Z')):
                    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
```

Example call:

```
f304([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 305

```python
def f305(nodes, edges):
    nodes = list(nodes)
    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)
    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))
        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 rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f305(['api', 'jobs', 'db', 'ui', 'proxy', 'cache', 'auth', 'worker'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')])
```

Output example:

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

### 306

```python
def f306(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 = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in repeats:
                repeats.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': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f306([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 307

```python
def f307(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(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)
    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
```

Example call:

```
f307([(3, 5), (6, 8), (15, 19), (19, 22), (29, 35), (34, 40), (44, 50), (49, 55), (60, 65)], 0)
```

Output example:

```
{"cover":38,"holes":[1,7,7,4,5],"longest":11,"segments":[[3,5],[6,8],[15,22],[29,40],[44,55],[60,65]]}
```

### 308

```python
def f308(board):
    board = list(board)
    found = 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 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
```

Example call:

```
f308(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 309

```python
def f309(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]
    ups = sum((1 for pos in range(1, 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
```

Example call:

```
f309([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 8, 80)
```

Output example:

```
{"best":147,"hits":[0,1,2,3,4,5,6,7],"rises":1,"sums":[147,147,140,138,135,128,125,131]}
```

### 310

```python
def f310(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors or rate0 <= rate0 + 0:
            factors[name0] = rate0
    matched = []
    for key, count in left:
        if key in factors and count > 0:
            matched.append((key, count * factors[key] + fee))
    matched.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted({key for key, count in left if key not in factors})
    returnvalue = {'items': [[key, value] for key, value in matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f310([('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["AN",30]],"missing":[],"total":316}
```

### 311

```python
def f311(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 or len(word) < 2:
            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
```

Example call:

```
f311(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 312

```python
def f312(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 = (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
```

Example call:

```
f312([('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1), ('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3)])
```

Output example:

```
{"bounds":[-1,-4,7,0],"end":[4,-1],"far":11,"revisits":[[4,0],[3,0],[2,0],[1,0],[0,0]],"steps":39}
```

### 313

```python
def f313(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices:
            prices[name0] = rate0
    combined = []
    for key, count in left[:20]:
        if key in prices and count > 0:
            combined.append((key, count * prices[key] + fee))
    combined.sort(key=lambda item: (-item[1], item[0]))
    unmatched = sorted((key for key, count in left if key not in prices))
    returnvalue = {'items': [[key, value] for key, value in combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f313([('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6), ('FP', 11), ('GQ', 5), ('HR', 4)], [('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5), ('FP', 5), ('GQ', 8), ('HR', 4)], 2)
```

Output example:

```
{"count":8,"items":[["DL",98],["FP",57],["CX",42],["GQ",42],["EV",32]],"missing":[],"total":331}
```

### 314

```python
def f314(board):
    board = list(board)
    found = set()
    pieces = []
    for row in range(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)
                        if len(found) >= 100:
                            continue
                        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
```

Example call:

```
f314(['####..', '#..#..', '..#.#.', '..###.', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[2,2],[0,0],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 315

```python
def f315(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 = []
            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)
            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
```

Example call:

```
f315(['####..', '#..##.', '..#.#.', '..##..', '##.#.#', '#..##.'])
```

Output example:

```
{"anchors":[[0,0],[2,2],[4,0],[4,5]],"count":4,"filled":18,"sizes":[8,6,3,1]}
```

### 316

```python
def f316(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        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, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    result = list(distance)
    edge = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': edge, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f316([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'G', 3)
```

Output example:

```
{"count":7,"depth":{"A":1,"B":2,"C":2,"D":3,"E":3,"F":3,"G":0},"frontier":["D","E","F"],"order":["G","A","B","C","D","E","F"]}
```

### 317

```python
def f317(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        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
```

Example call:

```
f317([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'B', 3)
```

Output example:

```
{"count":5,"depth":{"A":3,"B":0,"D":1,"E":1,"G":2},"frontier":["A"],"order":["B","D","E","G","A"]}
```

### 318

```python
def f318(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:
            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
```

Example call:

```
f318(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['helium'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"cyan":5,"delta":4,"ember":5,"frost":3,"garnet":3},"initials":{"a":5,"b":3,"c":5,"d":4,"e":5,"f":3,"g":3},"size":135,"top":["amber","cyan","ember","delta","blue"]}
```

### 319

```python
def f319(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:
            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
    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
```

Example call:

```
f319(['Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber', 'Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'], ['cyan'])
```

Output example:

```
{"counts":{"amber":5,"blue":3,"delta":4,"ember":5,"frost":3,"garnet":3,"helium":3},"initials":{"a":5,"b":3,"d":4,"e":5,"f":3,"g":3,"h":3},"size":133,"top":["amber","ember","delta","blue","frost"]}
```

### 320

```python
def f320(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]
    growth = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

Example call:

```
f320([22, 20, 22, 21, 21, 16, 15, 10, 22, 13, 20, 18, 14, 13, 21], 1, 80)
```

Output example:

```
{"best":22,"hits":[],"rises":4,"sums":[22,20,22,21,21,16,15,10,22,13,20,18,14,13,21]}
```

### Final Query

Give me the output of the final query without executing it!

```python
import json, re
from collections import deque
out = {}
nodes = list(('api', 'jobs', 'db', 'ui', 'proxy') + ('cache', 'auth', 'worker'))
edges = list((('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs')) + (('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui')))
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)}
route = record['aa'][0]
cases = {
    'auth': list((('E', 3), ('E', 2), ('W', 3), ('S', 2), ('E', 2), ('N', 2), ('S', 1)) + (('E', 3), ('E', 2), ('E', 1), ('S', 5), ('W', 3), ('W', 3), ('N', 3), ('E', 3))),
    'cache': list((('E', 3), ('E', 2), ('W', 6), ('S', 2), ('E', 2), ('N', 2), ('S', 1)) + (('E', 3), ('E', 2), ('E', 1), ('S', 3), ('W', 3), ('W', 3), ('N', 3), ('E', 3))),
}
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}
lines = list(('Frost, amber. blue garnet', 'Cyan, ember. garnet delta amber') + ('Delta, cyan. helium ember', 'Helium, ember. delta ember helium', 'Amber, frost. blue cyan', 'Garnet, cyan. blue delta amber', 'Amber, ember. cyan frost'))
route = record['bb']
cases = {
    16: ['cyan'],
    11: ['helium'],
}
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))}
edges = list((('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E')) + (('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')))
limit = 3
route = record['dd']
cases = {
    135: 'G',
    133: 'B',
}
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)}
spans = list(((3, 5), (6, 8), (15, 19), (19, 22), (29, 35)) + ((34, 40), (44, 50), (49, 55), (60, 65)))
route = record['dd']
cases = {
    5: 0,
    7: 1,
}
gap = cases[route]
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))}
route = record['cc']
cases = {
    39: list(('####..', '#..##.', '..#.#.') + ('..##..', '##.#.#', '#..##.')),
    38: 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)}
values = list((22, 20, 22, 21, 21, 16) + (15, 10, 22, 13, 20, 18, 14, 13, 21))
limit = 80
route = record['bb'][0][0]
cases = {
    2: 1,
    0: 8,
}
width = 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}
right = list((('AN', 7), ('BR', 5), ('CX', 5), ('DL', 8), ('EV', 5)) + (('FP', 5), ('GQ', 8), ('HR', 4)))
fee = 2
route = record['bb']
cases = {
    22: list((('AN', 4), ('BR', 2), ('CX', 8), ('DL', 12), ('EV', 6)) + (('FP', 11), ('GQ', 5), ('HR', 4))),
    147: list((('AN', 4), ('BR', 3), ('CX', 8), ('DL', 12), ('EV', 2)) + (('FP', 11), ('GQ', 5), ('HR', 4))),
}
left = cases[route]
joined = []
for key, count in left:
    matches = [rate for name, rate in right if name == key]
    if matches:
        joined.append([key, count * matches[0] + fee])
joined.sort(key=lambda item: (-item[1], item[0]))
rightkeys = {key for key, rate in right}
record = {'aa': joined[:5], 'bb': sum((item[1] for item in joined)), 'cc': sorted((key for key, count in left if key not in rightkeys)), 'dd': len(joined)}
out['aa'] = record['aa']
out['cc'] = record['cc']
out['bb'] = record['bb']
out['dd'] = record['dd']
print(json.dumps(out, separators=(",", ":"), sort_keys=True))
```