### 001

```python
def f1(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(min(64, len(values) - size + 1)):
        series.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] >= series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f1([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 002

```python
def f2(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop or len(word) < 2:
            continue
        frequency[word] = min(9, frequency.get(word, 0) + 1)
    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
```

```
f2(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 003

```python
def f3(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)
    finished = set()
    sequence = []
    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))
        if not available:
            break
        current = available[:1] if any((str(node).isupper() for node in nodes)) else available
        layers.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

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

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

### 004

```python
def f4(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f4([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 005

```python
def f5(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            score = value * abs(prices[group])
            matches.append((code, score))
            totals[group] = totals.get(group, 0) + score
            sumvalue += score
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(matches), 'total': sumvalue, 'groups': totals, 'top': [code for code, score in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f5([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 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])))
    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
```

```
f6([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 007

```python
def f7(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[: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
```

```
f7(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 008

```python
def f8(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}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    sequence = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': sequence, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f8([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 009

```python
def f9(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:
        if key in factors and count > 0:
            items.append((key, count * factors[key] + fee))
    items.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 items[:5]], 'total': sum((value for key, value in items)), 'missing': leftover, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f9([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 010

```python
def f10(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.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(children.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
```

```
f10([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 011

```python
def f11(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors and rate0 != 0:
            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
```

```
f11([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 012

```python
def f12(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' or (char == "'" and word):
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop or len(word) > 12:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    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
```

```
f12(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 013

```python
def f13(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 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
```

```
f13([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 014

```python
def f14(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    indexes = [pos for pos, value in enumerate(windows) 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': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f14([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 015

```python
def f15(rows, keep, prices):
    rows = list(rows)
    selected = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * prices[group]
            selected.append((code, score))
            totals[group] = totals.get(group, 0) + score
            grand += score
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(selected)), 'total': grand, 'groups': totals, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f15([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 016

```python
def f16(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, 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
```

```
f16([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 017

```python
def f17(rows, keep, prices):
    rows = list(rows)
    matches = []
    buckets = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * prices[group]
            matches.append((code, score))
            buckets[group] = buckets.get(group, 0) + score
            grand += score
    matches.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(dict.fromkeys(matches)), 'total': grand, 'groups': buckets, 'top': [code for code, score in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f17([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 018

```python
def f18(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in returns:
                returns.append(list(point))
            known.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f18([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 019

```python
def f19(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items:
        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
```

```
f19(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 020

```python
def f20(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)
    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 nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f20(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 021

```python
def f21(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop or len(word) < 2:
            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
```

```
f21(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 022

```python
def f22(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.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
                    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, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f22([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 023

```python
def f23(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] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    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
```

```
f23([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 024

```python
def f24(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        routes.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.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
                    queue.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[:3], 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f24([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 025

```python
def f25(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[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, len(totals)) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max([0] + totals), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f25([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 026

```python
def f26(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[:20]:
        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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f26([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 027

```python
def f27(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans, key=lambda pair: (pair[1], pair[0])):
        if not segments or left > segments[-1][1] + min(gap, 2):
            segments.append([left, right])
        else:
            segments[-1][1] = right
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f27([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 028

```python
def f28(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}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f28([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 029

```python
def f29(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < min(limit, 3):
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    listing = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': listing, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f29([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 030

```python
def f30(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 and (limit >= 0 or pos > 0)]
    ups = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f30([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 031

```python
def f31(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 = 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
```

```
f31([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 032

```python
def f32(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, 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': min(100, max((right - left for left, right in result)))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f32([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 033

```python
def f33(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[: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 repeats:
                repeats.append(list(point))
            visited.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': repeats[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f33([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 034

```python
def f34(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, 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
```

```
f34([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 035

```python
def f35(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
```

```
f35([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 036

```python
def f36(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 and (limit >= 0 or pos > 0)]
    increases = sum((1 for pos in range(1, min(65, len(totals))) if totals[pos] > totals[pos - 1]))
    returnvalue = {'sums': totals, 'best': max(totals), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f36([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 037

```python
def f37(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()
    listing = []
    groups = []
    while len(handled) < len(nodes):
        nextbatch = 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 nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            handled.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f37(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 038

```python
def f38(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f38([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 039

```python
def f39(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
    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
```

```
f39([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 040

```python
def f40(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 % 100):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in crossings:
                crossings.append(list(point))
            known.add(point)
            far = max(far, 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
```

```
f40([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 041

```python
def f41(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans, key=lambda pair: pair[0]):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    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': min(100, max((right - left for left, right in segments)))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f41([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 042

```python
def f42(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)
    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 initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f42(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 043

```python
def f43(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]
    growth = 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': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f43([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 044

```python
def f44(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    levels = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in levels:
                    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, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f44([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 045

```python
def f45(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = 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
```

```
f45([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 046

```python
def f46(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': min(256, max(windows)), 'hits': matches, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f46([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 047

```python
def f47(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 += 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
```

```
f47([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 048

```python
def f48(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)
    complete = set()
    result = []
    rounds = []
    while len(complete) < len(nodes) and len(complete) < 20:
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in complete), 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:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': rounds, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f48(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 049

```python
def f49(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] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(min(100, left - combined[pos - 1][1]))
    returnvalue = {'segments': combined, 'cover': sum((min(100, 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
```

```
f49([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 050

```python
def f50(rows, keep, prices):
    rows = list(rows)
    selected = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            charge = value * prices[group]
            selected.append((code, charge))
            totals[group] = totals.get(group, 0) + charge
            grand += charge
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(dict.fromkeys(selected)), 'total': grand, 'groups': totals, 'top': list(dict.fromkeys((code for code, charge in selected)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f50([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 051

```python
def f51(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    grand = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep:
            score = value * abs(prices[group])
            matches.append((code, score))
            totals[group] = totals.get(group, 0) + score
            grand += score
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(matches), 'total': grand, 'groups': totals, 'top': list(dict.fromkeys((code for code, score in matches)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f51([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 052

```python
def f52(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, 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
```

```
f52([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 053

```python
def f53(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)
    complete = set()
    sequence = []
    groups = []
    while len(complete) < len(nodes):
        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[:1] if any((str(node).isupper() for node in nodes)) else 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 initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f53(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 054

```python
def f54(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                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) > 12:
            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
```

```
f54(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 055

```python
def f55(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.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
```

```
f55([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 056

```python
def f56(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, 3 + (count - count))):
            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 = 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
```

```
f56([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 057

```python
def f57(values, width, limit):
    values = list(values)
    size = width
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': min(256, max(series)), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f57([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 058

```python
def f58(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = max(-64, min(64, x + dx))
            y += 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
```

```
f58([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 059

```python
def f59(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)]
    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
```

```
f59([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 060

```python
def f60(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
```

```
f60([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 061

```python
def f61(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:
        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
```

```
f61([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 062

```python
def f62(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]))
    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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f62([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

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

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

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 064

```python
def f64(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 = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = max(far, 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
```

```
f64([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 065

```python
def f65(rows, keep, ratemap):
    rows = list(rows)
    selected = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if state in keep and value >= 0:
            score = value * ratemap[group]
            selected.append((code, score))
            totals[group] = totals.get(group, 0) + score
            sumvalue += score
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': sumvalue, 'groups': totals, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f65([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 066

```python
def f66(rows, keep, factors):
    rows = list(rows)
    kept = []
    groupmap = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * abs(factors[group])
            kept.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            amount += cost
    kept.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(dict.fromkeys(kept)), 'total': amount, 'groups': groupmap, 'top': [code for code, cost in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f66([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 067

```python
def f67(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]
    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
```

```
f67([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 068

```python
def f68(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 += 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 = (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
```

```
f68([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 069

```python
def f69(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(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in crossings:
                crossings.append(list(point))
            visited.add(point)
            far = max(far, abs(x) + abs(y))
            lowx, highx = (max(-64, min(lowx, x)), min(64, max(highx, x)))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f69([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 070

```python
def f70(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] = 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
```

```
f70([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 071

```python
def f71(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]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f71([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 072

```python
def f72(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right:
        if name0 not in factors or rate0 <= rate0 + 0:
            factors[name0] = rate0
    combined = []
    for key, count in left:
        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
```

```
f72([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 073

```python
def f73(rows, keep, prices):
    rows = list(rows)
    selected = []
    totals = {}
    amount = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep and value != 0:
            score = value * prices[group]
            selected.append((code, score))
            totals[group] = totals.get(group, 0) + score
            amount += score
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(selected)), 'total': amount, 'groups': totals, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f73([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 074

```python
def f74(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f74([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 075

```python
def f75(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
    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
```

```
f75(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 076

```python
def f76(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() 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[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f76(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 077

```python
def f77(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = right
    gaps = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f77([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 078

```python
def f78(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)
    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
```

```
f78([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 079

```python
def f79(rows, keep, ratemap):
    rows = list(rows)
    selected = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep and value != 0:
            cost = value * abs(ratemap[group])
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            sumvalue += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': sumvalue, 'groups': totals, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f79([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 080

```python
def f80(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(min(count, 3 + (count - 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
```

```
f80([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 081

```python
def f81(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        children.setdefault(a, []).append(b)
    steps = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                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
```

```
f81([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 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
    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 = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 083

```python
def f83(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(min(64, len(values) - size + 1)):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(windows) if value >= limit and (limit >= 0 or pos > 0)]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f83([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 084

```python
def f84(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + max(0, gap):
            combined.append([left, right])
        else:
            combined[-1][1] = right
    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
```

```
f84([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 085

```python
def f85(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0} 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(routes.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f85([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 086

```python
def f86(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop or len(word) < 2:
            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': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f86(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 087

```python
def f87(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        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
```

```
f87(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 088

```python
def f88(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)
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f88([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 089

```python
def f89(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] < min(limit, 3):
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    pending.append(nxt)
    sequence = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f89([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 090

```python
def f90(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in routes[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
```

```
f90(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 091

```python
def f91(left, right, fee):
    left = list(left)
    factors = {}
    for name0, rate0 in right[:20]:
        if name0 not in factors and rate0 != 0:
            factors[name0] = rate0
    items = []
    for key, count in left:
        if key in factors and count > 0:
            items.append((key, count * factors[key] + fee))
    items.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 items[:5]], 'total': sum((value for key, value in items)), 'missing': leftover, 'count': len(items)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f91([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 092

```python
def f92(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:
        if word in stop or len(word) > 12:
            continue
        tallies[word] = tallies.get(word, 0) + 1
    sorteditems = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in sorteditems[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f92(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 093

```python
def f93(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = 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
```

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

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 094

```python
def f94(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    complete = set()
    result = []
    groups = []
    while len(complete) < len(nodes) and len(complete) < 20:
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in complete))
        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 routes[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
```

```
f94(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 095

```python
def f95(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(set(spans)):
        if not result or left > result[-1][1] + min(gap, 2):
            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((min(100, 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
```

```
f95([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 096

```python
def f96(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} if limit > 0 or limit < 0 else {}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if distance[cur] < min(limit, 3):
            for nxt in sorted(children.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    pending.append(nxt)
    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
```

```
f96([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 097

```python
def f97(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[0]) < 2):
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    work.append(nxt)
    listing = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': listing, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f97([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 098

```python
def f98(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]))
    leftover = 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': leftover, 'count': len({key for key, value in items})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f98([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 099

```python
def f99(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 (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)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f99([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 100

```python
def f100(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        routes.setdefault(a, []).append(b)
    steps = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    work.append(nxt)
    listing = list(steps)
    lastlevel = sorted((node for node in steps if steps[node] == max(steps.values())))
    returnvalue = {'order': listing, 'depth': steps, 'frontier': lastlevel, 'count': len(steps)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f100([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 101

```python
def f101(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(0, segments[-1][1], right)
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f101([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 102

```python
def f102(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)
    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
```

```
f102([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 103

```python
def f103(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    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
```

```
f103(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 104

```python
def f104(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[:64]) 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
```

```
f104([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 105

```python
def f105(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):
            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
```

```
f105([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 106

```python
def f106(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit and (limit >= 0 or pos > 0)]
    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
```

```
f106([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 107

```python
def f107(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
    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
```

```
f107([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 108

```python
def f108(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] = 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
```

```
f108([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 109

```python
def f109(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
```

```
f109([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 110

```python
def f110(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
    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
```

```
f110([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 111

```python
def f111(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    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 and (not nxt.startswith('Z')):
                    levels[nxt] = levels[cur] + 1
                    queue.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
```

```
f111([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 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)}
    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 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 113

```python
def f113(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)
    finished = set()
    listing = []
    layers = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

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

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

### 114

```python
def f114(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    handled = set()
    listing = []
    layers = []
    while len(handled) < len(nodes) and len(handled) < 20:
        nextbatch = sorted((node for node in nodes if indegree[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
        layers.append(current)
        for node in current:
            handled.add(node)
            listing.append(node)
        for node in current:
            for nxt in routes[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
```

```
f114(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 115

```python
def f115(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x = 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 = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 116

```python
def f116(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
```

```
f116([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 117

```python
def f117(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(windows) if value > limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f117([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 118

```python
def f118(rows, keep, factors):
    rows = list(rows)
    matches = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep} and value >= 0:
            score = value * factors[group]
            matches.append((code, score))
            totals[group] = totals.get(group, 0) + score
            grand += score
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(matches)), 'total': grand, 'groups': totals, 'top': [code for code, score in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f118([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 119

```python
def f119(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in edges[:16]:
        nextmap.setdefault(a, []).append(b)
    levels = {start: 0} if any((start in edge for edge in edges)) else {}
    queue = [start]
    while queue:
        cur = queue.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
                    queue.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
```

```
f119([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 120

```python
def f120(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    startdegree = dict(needs)
    finished = set()
    sequence = []
    rounds = []
    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))
        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]:
                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
```

```
f120(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 121

```python
def f121(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(min(count, 64)):
            x += dx
            y = max(-64, min(64, 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, 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
```

```
f121([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 122

```python
def f122(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
    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(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f122([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 123

```python
def f123(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:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    heads = {}
    for word, count in frequency.items():
        heads[word[0]] = heads.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in sorteditems[:5]], 'initials': heads, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f123(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 124

```python
def f124(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 100):
            x += 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 125

```python
def f125(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:
            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(min(100, left - result[pos - 1][1]))
    returnvalue = {'segments': result, 'cover': sum((right - left for left, right in result)), 'holes': gaps, 'longest': max((right - left for left, right in result))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f125([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 126

```python
def f126(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(windows) if value >= limit]
    growth = 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': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f126([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 127

```python
def f127(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
    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
```

```
f127([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 128

```python
def f128(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 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
```

```
f128([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 129

```python
def f129(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    levels = {start: 0}
    pending = [start]
    while pending:
        cur = pending.pop(0)
        if levels[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    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
```

```
f129([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 130

```python
def f130(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not segments or left > segments[-1][1] + gap:
            segments.append([left, right])
        else:
            segments[-1][1] = max(0, segments[-1][1], right)
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(min(100, left - segments[pos - 1][1]))
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f130([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 131

```python
def f131(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()
    sequence = []
    layers = []
    while len(complete) < len(nodes) and len(complete) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in complete))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f131(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 132

```python
def f132(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)
    complete = set()
    result = []
    layers = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in complete), 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 children[node]:
                indegree[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
```

```
f132(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 133

```python
def f133(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:
            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
```

```
f133([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 134

```python
def f134(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < 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
                    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
```

```
f134([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 135

```python
def f135(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:
        if before == after:
            continue
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    finished = set()
    sequence = []
    rounds = []
    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[:1] if any((str(node).isupper() for node in nodes)) else 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
```

```
f135(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 136

```python
def f136(spans, gap):
    spans = list(spans)
    segments = []
    for left, right in sorted(spans, key=lambda pair: (pair[1], pair[0])):
        if not segments or left > segments[-1][1] + gap % 5:
            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
```

```
f136([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 137

```python
def f137(rows, keep, prices):
    rows = list(rows)
    selected = []
    buckets = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep and value != 0:
            score = value * prices[group]
            selected.append((code, score))
            buckets[group] = buckets.get(group, 0) + score
            amount += score
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': buckets, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f137([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 138

```python
def f138(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]))
    leftover = 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': leftover, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f138([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 139

```python
def f139(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]))
    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
```

```
f139([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 140

```python
def f140(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(windows) if value >= limit]
    ups = sum((1 for pos in range(1, len(windows)) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f140([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 141

```python
def f141(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)
    finished = set()
    result = []
    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)
            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
```

```
f141(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 142

```python
def f142(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in handled))
        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 routes[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
```

```
f142(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 143

```python
def f143(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(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, 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
```

```
f143([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 144

```python
def f144(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value >= limit]
    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
```

```
f144([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 145

```python
def f145(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    items = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                items.append(word)
                word = ''
        if word:
            items.append(word)
    for word in items[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    starts = {}
    for word, count in wordmap.items():
        starts[word[0]] = starts.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in wordmap.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f145(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 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 % 100):
            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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 147

```python
def f147(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
    combined = []
    for key, count in left:
        if key in ratemap:
            combined.append((key, count * ratemap[key] + fee))
    combined.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 combined[:5]], 'total': sum((value for key, value in combined)), 'missing': unmatched, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f147([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 148

```python
def f148(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 and (limit >= 0 or pos > 0)]
    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
```

```
f148([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 149

```python
def f149(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    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, 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 150

```python
def f150(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x = 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 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
```

```
f150([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 151

```python
def f151(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)
    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
```

```
f151([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 152

```python
def f152(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if distance[cur] < 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
                    work.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
```

```
f152([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 153

```python
def f153(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()
    listing = []
    layers = []
    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
        layers.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': listing, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f153(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 154

```python
def f154(rows, keep, factors):
    rows = list(rows)
    selected = []
    groupmap = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            charge = value * abs(factors[group])
            selected.append((code, charge))
            groupmap[group] = groupmap.get(group, 0) + charge
            amount += charge
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': groupmap, 'top': [code for code, charge in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f154([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 155

```python
def f155(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()
    listing = []
    groups = []
    while len(finished) < len(nodes) and len(finished) < 20:
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': listing, 'batches': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(listing)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f155(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 156

```python
def f156(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        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]))
    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
```

```
f156([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 157

```python
def f157(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
    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
```

```
f157(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 158

```python
def f158(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]))
    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
```

```
f158([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 159

```python
def f159(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + min(gap, 2):
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    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
```

```
f159([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 160

```python
def f160(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[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    sorteditems = 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 sorteditems[:5]], 'initials': starts, 'size': sum((len(word) * count for word, count in frequency.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f160(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 161

```python
def f161(rows, keep, factors):
    rows = list(rows)
    selected = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            cost = value * factors[group]
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            sumvalue += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': sumvalue, 'groups': totals, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f161([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 162

```python
def f162(rows, keep, ratemap):
    rows = list(rows)
    matches = []
    groupmap = {}
    sumvalue = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep:
            cost = value * abs(ratemap[group])
            matches.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            sumvalue += cost
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(matches), 'total': sumvalue, 'groups': groupmap, 'top': [code for code, cost in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f162([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 163

```python
def f163(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.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
                    pending.append(nxt)
    result = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': result, 'depth': distance, 'frontier': furthest[:3], 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f163([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 164

```python
def f164(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[:20]:
        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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f164([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 165

```python
def f165(rows, keep, prices):
    rows = list(rows)
    kept = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep and value != 0:
            cost = value * prices[group]
            kept.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            grand += cost
    kept.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(kept), 'total': grand, 'groups': totals, 'top': list(dict.fromkeys((code for code, cost in kept)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f165([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 166

```python
def f166(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    handled = set()
    result = []
    layers = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in handled))
        if not nextbatch:
            break
        current = nextbatch
        layers.append(current)
        for node in current:
            handled.add(node)
            result.append(node)
        for node in current:
            for nxt in routes[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
```

```
f166(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 167

```python
def f167(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used = min(64, used + 1)
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 168

```python
def f168(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * prices[group]
            matches.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            grand += cost
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(matches), 'total': grand, 'groups': totals, 'top': [code for code, cost in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f168([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 169

```python
def f169(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)
    handled = set()
    sequence = []
    groups = []
    while len(handled) < len(nodes):
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in handled))
        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 nextmap[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
```

```
f169(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 170

```python
def f170(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        tallies[word] = min(9, 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
```

```
f170(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 171

```python
def f171(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]))
    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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f171([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 172

```python
def f172(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:
            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
```

```
f172(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 173

```python
def f173(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices and rate0 != 0:
            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
```

```
f173([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 174

```python
def f174(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    finished = set()
    result = []
    rounds = []
    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))
        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 nextmap[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f174(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 175

```python
def f175(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        routes[a].append(b)
        indegree[b] += 1
    startdegree = dict(indegree)
    complete = set()
    sequence = []
    layers = []
    while len(complete) < len(nodes):
        nextbatch = sorted((node for node in nodes if indegree[node] == 0 and node not in complete), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f175(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 176

```python
def f176(left, right, fee):
    left = list(left)
    prices = {}
    for name0, rate0 in right:
        if name0 not in prices and rate0 != 0:
            prices[name0] = rate0
    items = []
    for key, count in left:
        if key in prices and count > 0:
            items.append((key, count * prices[key] + fee))
    items.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 items[:5]], 'total': sum((value for key, value in items)), 'missing': unmatched, 'count': len({key for key, value in items})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f176([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 177

```python
def f177(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[:64]) if value >= limit]
    ups = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': min(256, max(series)), 'hits': indexes, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f177([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 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]))
    positions = [pos for pos, value in enumerate(totals) if value >= limit and (limit >= 0 or pos > 0)]
    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': positions, 'rises': ups}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f178([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 179

```python
def f179(rows, keep, factors):
    rows = list(rows)
    kept = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            cost = value * factors[group]
            kept.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            sumvalue += cost
    kept.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(kept), 'total': sumvalue, 'groups': totals, 'top': [code for code, cost in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f179([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 180

```python
def f180(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]))
    leftover = 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': leftover, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f180([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 181

```python
def f181(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.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] < 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)
    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
```

```
f181([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 182

```python
def f182(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap or rate0 <= rate0 + 0:
            ratemap[name0] = rate0
    matched = []
    for key, count in left[:20]:
        if key in ratemap:
            matched.append((key, count * ratemap[key] + fee))
    matched.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 matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f182([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 183

```python
def f183(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    positions = [pos for pos, value in enumerate(windows) if value > limit]
    increases = sum((1 for pos in range(1, len(windows)) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max([0] + windows), 'hits': positions, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f183([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 184

```python
def f184(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        children.setdefault(a, []).append(b)
    steps = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, []))[:20]:
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.append(nxt)
    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
```

```
f184([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 185

```python
def f185(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
    rootsource = dict(incoming)
    complete = set()
    sequence = []
    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=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f185(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 186

```python
def f186(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    levels = {start: 0} if any((start in edge for edge in edges)) else {} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    sequence = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f186([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 187

```python
def f187(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 and count > 0:
            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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f187([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 188

```python
def f188(rows, keep, prices):
    rows = list(rows)
    selected = []
    buckets = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep and value >= 0:
            cost = value * prices[group]
            selected.append((code, cost))
            buckets[group] = buckets.get(group, 0) + cost
            amount += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(selected)), 'total': amount, 'groups': buckets, 'top': list(dict.fromkeys((code for code, cost in selected)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f188([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 189

```python
def f189(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
```

```
f189([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 190

```python
def f190(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    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
```

```
f190(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 191

```python
def f191(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]
    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
```

```
f191([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 192

```python
def f192(nodes, edges):
    nodes = list(nodes)
    indegree = {node: 0 for node in nodes}
    nextmap = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        nextmap[a].append(b)
        indegree[b] += 1
    rootsource = dict(indegree)
    handled = set()
    listing = []
    groups = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if indegree[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]:
                indegree[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
```

```
f192(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 193

```python
def f193(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    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)
    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
```

```
f193([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 194

```python
def f194(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ranking = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    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
```

```
f194(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 195

```python
def f195(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) > 12:
            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': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f195(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 196

```python
def f196(lines, stop):
    lines = list(lines)
    wordmap = {}
    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:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    ordered = sorted(wordmap.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in wordmap.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': wordmap, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': min(256, sum((len(word) * count for word, count in wordmap.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f196(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 197

```python
def f197(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:
        if key in prices:
            items.append((key, count * prices[key] + fee))
    items.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 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
```

```
f197([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 198

```python
def f198(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([0] + series), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f198([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 199

```python
def f199(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 % 100):
            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
```

```
f199([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 200

```python
def f200(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[:20]:
        if key in ratemap:
            matched.append((key, count * ratemap[key] + fee))
    matched.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 matched[:5]], 'total': sum((value for key, value in matched)), 'missing': unmatched, 'count': len(matched)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f200([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 201

```python
def f201(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)
    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
```

```
f201([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 202

```python
def f202(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
    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
```

```
f202(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 203

```python
def f203(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(min(count, 3 + (count - count))):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in known and list(point) not in crossings:
                crossings.append(list(point))
            known.add(point)
            far = max(far, min(20, abs(x) + abs(y)))
            lowx, highx = (min(lowx, x), max(highx, x))
            lowy, highy = (min(lowy, y), max(highy, y))
    returnvalue = {'end': [x, y], 'far': far, 'revisits': crossings[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f203([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 204

```python
def f204(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    combined = []
    for key, count in left:
        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
```

```
f204([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 205

```python
def f205(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    complete = set()
    sequence = []
    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=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f205(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 206

```python
def f206(rows, keep, factors):
    rows = list(rows)
    kept = []
    groupmap = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * factors[group]
            kept.append((code, score))
            groupmap[group] = groupmap.get(group, 0) + score
            sumvalue += score
    kept.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(kept)), 'total': sumvalue, 'groups': groupmap, 'top': list(dict.fromkeys((code for code, score in kept)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f206([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 207

```python
def f207(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                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]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f207(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 208

```python
def f208(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms[:64]:
        if word in stop:
            continue
        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
```

```
f208(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 209

```python
def f209(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    found = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in found and list(point) not in returns:
                returns.append(list(point))
            found.add(point)
            far = max(far, 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
```

```
f209([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 210

```python
def f210(nodes, edges):
    nodes = list(nodes)
    needs = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        needs[b] += 1
    initial = dict(needs)
    complete = set()
    sequence = []
    layers = []
    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
        layers.append(current)
        for node in current:
            complete.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f210(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 211

```python
def f211(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count % 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 = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 212

```python
def f212(rows, keep, ratemap):
    rows = list(rows)
    kept = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if str(state).lower() in {str(item).lower() for item in keep}:
            score = value * ratemap[group]
            kept.append((code, score))
            totals[group] = totals.get(group, 0) + score
            sumvalue += score
    kept.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(kept), 'total': sumvalue, 'groups': totals, 'top': [code for code, score in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f212([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 213

```python
def f213(moves):
    moves = list(moves)
    step = {'N': (0, 1), 'E': (1, 0), 'S': (0, -1), 'W': (-1, 0)}
    x = 0
    y = 0
    known = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(min(count, 64)):
            x += dx
            y += dy
            used += 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
```

```
f213([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 214

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

```
f214([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 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))]
    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 = []
    layers = []
    while len(handled) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in handled), reverse=len(nodes) > 20)
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

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

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

### 216

```python
def f216(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(min(100, left - combined[pos - 1][1]))
    returnvalue = {'segments': combined, 'cover': sum((min(100, 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
```

```
f216([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 217

```python
def f217(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges:
        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, [])):
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.append(nxt)
    sequence = list(levels)
    furthest = sorted((node for node in levels if levels[node] == max(levels.values())))
    returnvalue = {'order': sequence, 'depth': levels, 'frontier': furthest, 'count': len(levels)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f217([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 218

```python
def f218(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
```

```
f218([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 219

```python
def f219(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)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[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
        layers.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f219(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 220

```python
def f220(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
```

```
f220(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 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
    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 = 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 = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 222

```python
def f222(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = 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
```

```
f222([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 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]))
    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
```

```
f223([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 224

```python
def f224(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        if name0 not in ratemap:
            ratemap[name0] = rate0
    matched = []
    for key, count in left[:20]:
        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
```

```
f224([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 225

```python
def f225(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
    rootsource = dict(incoming)
    finished = set()
    result = []
    groups = []
    while len(finished) < len(nodes) and len(finished) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=len(nodes) > 20)
        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 nextmap[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
```

```
f225(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 226

```python
def f226(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    initial = dict(incoming)
    finished = set()
    sequence = []
    groups = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if incoming[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if initial[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f226(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 227

```python
def f227(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]))
    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({key for key, value in matched})}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f227([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 228

```python
def f228(rows, keep, ratemap):
    rows = list(rows)
    selected = []
    totals = {}
    amount = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep and value >= 0:
            score = value * ratemap[group]
            selected.append((code, score))
            totals[group] = totals.get(group, 0) + score
            amount += score
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': totals, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f228([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 229

```python
def f229(rows, keep, prices):
    rows = list(rows)
    kept = []
    totals = {}
    amount = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep:
            cost = value * prices[group]
            kept.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            amount += cost
    kept.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(kept), 'total': amount, 'groups': totals, 'top': [code for code, cost in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f229([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 230

```python
def f230(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    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)
    complete = set()
    sequence = []
    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)
            sequence.append(node)
        for node in current:
            for nxt in children[node]:
                needs[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

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

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

### 231

```python
def f231(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
    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
```

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

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 232

```python
def f232(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    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)
    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
```

```
f232([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 233

```python
def f233(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
```

```
f233([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 234

```python
def f234(rows, keep, factors):
    rows = list(rows)
    selected = []
    buckets = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * abs(factors[group])
            selected.append((code, score))
            buckets[group] = buckets.get(group, 0) + score
            grand += score
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': grand, 'groups': buckets, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f234([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 235

```python
def f235(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, []))[:20]:
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.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
```

```
f235([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 236

```python
def f236(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        if word in stop:
            continue
        tallies[word] = min(9, tallies.get(word, 0) + 1)
    ordered = sorted(tallies.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in tallies.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': tallies, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': sum((len(word) * count for word, count in tallies.items()))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f236(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 237

```python
def f237(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        wordmap[word] = wordmap.get(word, 0) + 1
    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
```

```
f237(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 238

```python
def f238(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)
    complete = set()
    result = []
    rounds = []
    while len(complete) < len(nodes):
        available = sorted((node for node in nodes if indegree[node] == 0 and node not in complete))
        if not available:
            break
        current = available
        rounds.append(current)
        for node in current:
            complete.add(node)
            result.append(node)
        for node in current:
            for nxt in children[node]:
                indegree[nxt] -= 1
    returnvalue = {'order': result, 'batches': rounds, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f238(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 239

```python
def f239(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):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch
        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
```

```
f239(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 240

```python
def f240(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            score = value * prices[group]
            matches.append((code, score))
            totals[group] = totals.get(group, 0) + score
            sumvalue += score
    matches.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(dict.fromkeys(matches)), 'total': sumvalue, 'groups': totals, 'top': [code for code, score in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f240([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 241

```python
def f241(rows, keep, ratemap):
    rows = list(rows)
    matches = []
    groupmap = {}
    grand = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep:
            cost = value * ratemap[group]
            matches.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            grand += cost
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(matches)), 'total': grand, 'groups': groupmap, 'top': list(dict.fromkeys((code for code, cost in matches)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f241([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 242

```python
def f242(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    routes = {node: [] for node in nodes}
    for before, after in edges:
        a, b = (before, after)
        routes[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    finished = set()
    sequence = []
    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)
            sequence.append(node)
        for node in current:
            for nxt in routes[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f242(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 243

```python
def f243(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    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
```

```
f243(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 244

```python
def f244(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    steps = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(nextmap.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    queue.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
```

```
f244([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 245

```python
def f245(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, 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
```

```
f245([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 246

```python
def f246(spans, gap):
    spans = list(spans)
    result = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not result or left > result[-1][1] + gap:
            result.append([left, right])
        else:
            result[-1][1] = max(result[-1][1], right)
    gaps = []
    for pos in range(1, len(result)):
        left = result[pos][0]
        gaps.append(min(100, left - result[pos - 1][1]))
    returnvalue = {'segments': result, 'cover': sum((min(100, 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
```

```
f246([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 247

```python
def f247(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    items = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[: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
    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
```

```
f247(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 248

```python
def f248(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(min(count, 3 + (count - 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
```

```
f248([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 249

```python
def f249(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, 3 + (count - count))):
            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 = (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
```

```
f249([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 250

```python
def f250(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
```

```
f250(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 251

```python
def f251(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])))
    indexes = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f251([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 252

```python
def f252(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] = min(9, 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': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f252(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 253

```python
def f253(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(((max(0, a), max(0, b)) for a, b in spans)):
        if not combined or left > combined[-1][1] + gap % 5:
            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
```

```
f253([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 254

```python
def f254(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in edges[:16]:
        children.setdefault(a, []).append(b)
    steps = {start: 0} if any((start in edge for edge in edges)) else {} if limit > 0 or limit < 0 else {}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in sorted(children.get(cur, [])):
                if nxt not in steps:
                    steps[nxt] = steps[cur] + 1
                    work.append(nxt)
    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
```

```
f254([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 255

```python
def f255(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
    ordered = sorted(frequency.items(), key=lambda item: (-item[1], item[0]))
    letters = {}
    for word, count in frequency.items():
        letters[word[0]] = letters.get(word[0], 0) + count
    returnvalue = {'counts': frequency, 'top': [word for word, count in ordered[:5]], 'initials': letters, 'size': min(256, sum((len(word) * count for word, count in frequency.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f255(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 256

```python
def f256(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum(values[pos:pos + size]))
    matches = [pos for pos, value in enumerate(windows[:64]) if value > limit]
    increases = sum((1 for pos in range(1, min(65, len(windows))) if windows[pos] > windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f256([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 257

```python
def f257(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):
            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, 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': returns[:5], 'bounds': [lowx, lowy, highx, highy], 'steps': used}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f257([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 258

```python
def f258(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        children.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in (node for node in sorted(children.get(cur, [])) if len(str(node)) == 1):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f258([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 259

```python
def f259(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]
    growth = sum((1 for pos in range(1, len(series)) if series[pos] >= series[pos - 1]))
    returnvalue = {'sums': series, 'best': max(series), 'hits': matches, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f259([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 260

```python
def f260(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[: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
```

```
f260(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 261

```python
def f261(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    distance = {start: 0}
    pending = [start]
    while pending:
        cur = pending.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
                    pending.append(nxt)
    listing = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': listing, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f261([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 262

```python
def f262(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(min(count, 3 + (count - 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
```

```
f262([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1)])
```

```
{"bounds":[-1,-1,6,4],"end":[4,4],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":28}
```

### 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
    visited = {(0, 0)}
    returns = []
    far = 0
    lowx = highx = lowy = highy = 0
    used = 0
    for direction, count in moves:
        dx, dy = step[direction]
        for turn in range(count):
            x += dx
            y += dy
            used += 1
            point = (x, y)
            if point in visited and list(point) not in returns:
                returns.append(list(point))
            visited.add(point)
            far = 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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 264

```python
def f264(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * prices[group]
            matches.append((code, score))
            totals[group] = totals.get(group, 0) + score
            sumvalue += score
    matches.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(matches), 'total': sumvalue, 'groups': totals, 'top': [code for code, score in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f264([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 265

```python
def f265(rows, keep, prices):
    rows = list(rows)
    selected = []
    buckets = {}
    grand = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            score = value * prices[group]
            selected.append((code, score))
            buckets[group] = buckets.get(group, 0) + score
            grand += score
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': grand, 'groups': buckets, 'top': [code for code, score in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f265([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 266

```python
def f266(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} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if levels[cur] < limit:
            for nxt in sorted(routes.get(cur, []))[:20]:
                if nxt not in levels:
                    levels[nxt] = levels[cur] + 1
                    queue.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
```

```
f266([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 267

```python
def f267(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(series) if value >= limit]
    increases = sum((1 for pos in range(1, len(series)) if series[pos] > series[pos - 1]))
    returnvalue = {'sums': series, 'best': max([0] + series), 'hits': matches, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f267([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 268

```python
def f268(rows, keep, prices):
    rows = list(rows)
    matches = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * abs(prices[group])
            matches.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            grand += cost
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(matches), 'total': grand, 'groups': totals, 'top': [code for code, cost in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f268([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 269

```python
def f269(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right:
        if name0 not in ratemap and rate0 != 0:
            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
```

```
f269([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 270

```python
def f270(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] + min(gap, 2):
            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(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
```

```
f270([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 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 % 5:
            segments.append([left, right])
        else:
            segments[-1][1] = right
    spaces = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        spaces.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': spaces, 'longest': min(100, max((right - left for left, right in segments)))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f271([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 272

```python
def f272(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:20]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        if word in stop:
            continue
        frequency[word] = frequency.get(word, 0) + 1
    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
```

```
f272(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 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
    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 % 100):
            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 = (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
```

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

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 274

```python
def f274(values, width, limit):
    values = list(values)
    size = width if width > 1 or width < 1 else 2
    series = []
    for pos in range(len(values) - size + 1):
        series.append(sum(values[pos:pos + size]))
    indexes = [pos for pos, value in enumerate(series) if value >= limit]
    increases = 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': indexes, 'rises': increases}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f274([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 275

```python
def f275(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]))
    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
```

```
f275([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 276

```python
def f276(rows, keep, factors):
    rows = list(rows)
    kept = []
    totals = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep and value != 0:
            cost = value * factors[group]
            kept.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            amount += cost
    kept.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(kept), 'total': amount, 'groups': totals, 'top': [code for code, cost in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f276([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 277

```python
def f277(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': max([0] + totals), 'hits': indexes, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f277([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 278

```python
def f278(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(spans):
        if not combined or left > combined[-1][1] + min(gap, 2):
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    gaps = []
    for pos in range(1, min(50, len(combined))):
        left = combined[pos][0]
        gaps.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': gaps, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f278([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 279

```python
def f279(nodes, edges):
    nodes = list(nodes)
    nodes = [node for node in nodes if node not in nodes or any((node in edge for edge in edges))]
    indegree = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        indegree[b] += 1
    initial = dict(indegree)
    finished = set()
    listing = []
    groups = []
    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))
        if not nextbatch:
            break
        current = nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            listing.append(node)
        for node in current:
            for nxt in children[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
```

```
f279(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 280

```python
def f280(edges, start, limit):
    edges = list(edges)
    children = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        children.setdefault(a, []).append(b)
    distance = {start: 0} if limit > 0 or limit < 0 else {}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < 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
```

```
f280([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 281

```python
def f281(lines, stop):
    lines = list(lines)
    tallies = {}
    stop = {word.lower() for word in stop}
    tokens = []
    for line in lines:
        text = line.lower()
        word = ''
        for char in text[:64]:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                tokens.append(word)
                word = ''
        if word:
            tokens.append(word)
    for word in tokens[:64]:
        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
```

```
f281(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 282

```python
def f282(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)
    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
```

```
f282([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 283

```python
def f283(rows, keep, prices):
    rows = list(rows)
    selected = []
    groupmap = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * prices[group]
            selected.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            amount += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': groupmap, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f283([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 284

```python
def f284(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)
    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
```

```
f284([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 285

```python
def f285(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] + min(gap, 2):
            segments.append([left, right])
        else:
            segments[-1][1] = max(0, segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': max((right - left for left, right in segments))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f285([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 286

```python
def f286(rows, keep, prices):
    rows = list(rows)
    matches = []
    buckets = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * prices[group]
            matches.append((code, cost))
            buckets[group] = buckets.get(group, 0) + cost
            amount += cost
    matches.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(matches)), 'total': amount, 'groups': buckets, 'top': list(dict.fromkeys((code for code, cost in matches)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f286([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 287

```python
def f287(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, 3 + (count - 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 = (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
```

```
f287([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 288

```python
def f288(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:
        if key in prices:
            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
```

```
f288([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 289

```python
def f289(left, right, fee):
    left = list(left)
    ratemap = {}
    for name0, rate0 in right[:20]:
        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]))
    leftover = 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': leftover, 'count': len(combined)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f289([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 290

```python
def f290(rows, keep, prices):
    rows = list(rows)
    kept = []
    groupmap = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep and value >= 0:
            cost = value * prices[group]
            kept.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            grand += cost
    kept.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(kept), 'total': grand, 'groups': groupmap, 'top': [code for code, cost in kept[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f290([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 291

```python
def f291(rows, keep, prices):
    rows = list(rows)
    selected = []
    groupmap = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * prices[group]
            selected.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            amount += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': groupmap, 'top': list(dict.fromkeys((code for code, cost in selected)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f291([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 292

```python
def f292(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)
    complete = set()
    sequence = []
    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)
            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
```

```
f292(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 293

```python
def f293(rows, keep, prices):
    rows = list(rows)
    selected = []
    groupmap = {}
    sumvalue = 0
    for code, group, state, value in (row for pos, row in enumerate(rows) if pos == rows.index(row) or pos < len(rows) - (len(rows) - rows.index(row))):
        if state in keep:
            cost = value * prices[group]
            selected.append((code, cost))
            groupmap[group] = groupmap.get(group, 0) + cost
            sumvalue += cost
    selected.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(selected), 'total': sumvalue, 'groups': groupmap, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f293([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 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:
            segments.append([left, right])
        else:
            segments[-1][1] = max(segments[-1][1], right)
    gaps = []
    for pos in range(1, len(segments)):
        left = segments[pos][0]
        gaps.append(left - segments[pos - 1][1])
    returnvalue = {'segments': segments, 'cover': sum((right - left for left, right in segments)), 'holes': gaps, 'longest': min(100, max((right - left for left, right in segments)))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f294([(3, 5), (8, 12), (15, 17), (19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":34,"holes":[3,3,5,8,3,4],"longest":9,"segments":[[3,5],[8,12],[15,24],[29,36],[44,46],[49,56],[60,63]]}
```

### 295

```python
def f295(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
    rootsource = 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), 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]:
                needs[nxt] -= 1
    returnvalue = {'order': result, 'batches': layers, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f295(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 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
    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):
            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
```

```
f296([('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2), ('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2)])
```

```
{"bounds":[-1,-1,6,4],"end":[5,2],"far":9,"revisits":[[0,0],[2,0],[5,-1],[4,-1],[6,-1]],"steps":29}
```

### 297

```python
def f297(edges, start, limit):
    edges = list(edges)
    routes = {}
    for a, b in (edge for edge in edges if len(edge[1]) < 2):
        routes.setdefault(a, []).append(b)
    distance = {start: 0}
    queue = [start]
    while queue:
        cur = queue.pop(0)
        if distance[cur] < limit:
            for nxt in sorted(routes.get(cur, [])):
                if nxt not in distance:
                    distance[nxt] = distance[cur] + 1
                    queue.append(nxt)
    sequence = list(distance)
    furthest = sorted((node for node in distance if distance[node] == max(distance.values())))
    returnvalue = {'order': sequence, 'depth': distance, 'frontier': furthest, 'count': len(distance)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f297([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 4)
```

```
{"count":8,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2,"G":3,"H":3},"frontier":["G","H"],"order":["A","B","C","D","E","F","G","H"]}
```

### 298

```python
def f298(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(len(values) - size + 1):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    positions = [pos for pos, value in enumerate(windows) if value > limit]
    growth = sum((1 for pos in range(1, len(windows)) if windows[pos] >= windows[pos - 1]))
    returnvalue = {'sums': windows, 'best': max(windows), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f298([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 299

```python
def f299(spans, gap):
    spans = list(spans)
    combined = []
    for left, right in sorted(set(spans)):
        if not combined or left > combined[-1][1] + gap % 5:
            combined.append([left, right])
        else:
            combined[-1][1] = max(combined[-1][1], right)
    spaces = []
    for pos in range(1, len(combined)):
        left = combined[pos][0]
        spaces.append(left - combined[pos - 1][1])
    returnvalue = {'segments': combined, 'cover': sum((right - left for left, right in combined)), 'holes': spaces, 'longest': max((right - left for left, right in combined))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f299([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 300

```python
def f300(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 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
```

```
f300([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 301

```python
def f301(values, width, limit):
    values = list(values)
    size = width
    windows = []
    for pos in range(min(64, len(values) - size + 1)):
        windows.append(sum((max(item, 0) for item in values[pos:pos + size])))
    matches = [pos for pos, value in enumerate(windows[: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(windows), 'hits': matches, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f301([17, 4, 21, 24, 17, 18, 11, 12, 7, 7, 13, 19, 12, 6, 21], 4, 83)
```

```
{"best":80,"hits":[],"rises":5,"sums":[66,66,80,70,58,48,37,39,46,51,50,58]}
```

### 302

```python
def f302(rows, keep, factors):
    rows = list(rows)
    selected = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep} and value >= 0:
            cost = value * factors[group]
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            grand += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': grand, 'groups': totals, 'top': list(dict.fromkeys((code for code, cost in selected)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f302([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 303

```python
def f303(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
```

```
f303([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 2)
```

```
{"count":6,"items":[["DL",56],["CX",38],["BR",34],["GQ",32],["EV",22]],"missing":["AN","HR"],"total":204}
```

### 304

```python
def f304(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 and count > 0:
            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
```

```
f304([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 305

```python
def f305(lines, stop):
    lines = list(lines)
    wordmap = {}
    stop = {word.lower() for word in stop}
    terms = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text:
            if 'a' <= char <= 'z':
                word += char
            elif word:
                terms.append(word)
                word = ''
        if word:
            terms.append(word)
    for word in terms:
        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': min(256, sum((len(word) * count for word, count in wordmap.items())))}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f305(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan quartz', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"quartz":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"q":1},"size":145,"top":["helium","amber","cyan","ember","frost"]}
```

### 306

```python
def f306(rows, keep, prices):
    rows = list(rows)
    kept = []
    buckets = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if state in keep:
            score = value * abs(prices[group])
            kept.append((code, score))
            buckets[group] = buckets.get(group, 0) + score
            sumvalue += score
    kept.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(kept), 'total': sumvalue, 'groups': buckets, 'top': list(dict.fromkeys((code for code, score in kept)))[:3]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f306([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 307

```python
def f307(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([0] + series), 'hits': positions, 'rises': growth}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f307([17, 4, 21, 24, 14, 18, 11, 12, 7, 7, 17, 19, 12, 6, 21], 4, 82)
```

```
{"best":77,"hits":[],"rises":5,"sums":[66,63,77,67,55,48,37,43,50,55,54,58]}
```

### 308

```python
def f308(edges, start, limit):
    edges = list(edges)
    nextmap = {}
    for a, b in (edge for edge in edges if edge[0] <= edge[1]):
        nextmap.setdefault(a, []).append(b)
    steps = {start: 0}
    work = [start]
    while work:
        cur = work.pop(0)
        if steps[cur] < limit:
            for nxt in (node for node in sorted(nextmap.get(cur, [])) if len(str(node)) == 1):
                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
```

```
f308([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 309

```python
def f309(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
    rootsource = dict(needs)
    finished = set()
    result = []
    groups = []
    while len(finished) < len(nodes):
        nextbatch = sorted((node for node in nodes if needs[node] == 0 and node not in finished), reverse=any((str(node).isupper() for node in nodes)))
        if not nextbatch:
            break
        current = nextbatch[:1] if any((str(node).isupper() for node in nodes)) else nextbatch
        groups.append(current)
        for node in current:
            finished.add(node)
            result.append(node)
        for node in current:
            for nxt in nextmap[node]:
                needs[nxt] -= 1
    returnvalue = {'order': result, 'batches': groups, 'roots': sorted((node for node in nodes if rootsource[node] == 0)), 'count': len(result)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f309(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth')])
```

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

### 310

```python
def f310(lines, stop):
    lines = list(lines)
    frequency = {}
    stop = {str(word) for word in stop}
    tokens = []
    for line in lines[:32]:
        text = line.lower()
        word = ''
        for char in text[: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
```

```
f310(['Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan', 'Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'], ['garnet'])
```

```
{"counts":{"amber":5,"blue":2,"cyan":5,"delta":2,"ember":4,"frost":4,"helium":6,"vivid":1},"initials":{"a":5,"b":2,"c":5,"d":2,"e":4,"f":4,"h":6,"v":1},"size":144,"top":["helium","amber","cyan","ember","frost"]}
```

### 311

```python
def f311(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] = 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
```

```
f311([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### 312

```python
def f312(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
    startdegree = dict(incoming)
    handled = set()
    sequence = []
    layers = []
    while len(handled) < len(nodes) and len(handled) < 20:
        available = sorted((node for node in nodes if incoming[node] == 0 and node not in handled), reverse=any((str(node).isupper() for node in nodes)))
        if not available:
            break
        current = available
        layers.append(current)
        for node in current:
            handled.add(node)
            sequence.append(node)
        for node in current:
            for nxt in nextmap[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': layers, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f312(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 313

```python
def f313(nodes, edges):
    nodes = list(nodes)
    incoming = {node: 0 for node in nodes}
    children = {node: [] for node in nodes}
    for before, after in edges:
        if before == after:
            continue
        a, b = (before, after)
        children[a].append(b)
        incoming[b] += 1
    startdegree = dict(incoming)
    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 children[node]:
                incoming[nxt] -= 1
    returnvalue = {'order': sequence, 'batches': groups, 'roots': sorted((node for node in nodes if startdegree[node] == 0)), 'count': len(sequence)}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f313(['cache', 'ui', 'proxy', 'auth', 'api', 'worker', 'jobs', 'db'], [('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs'), ('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db')])
```

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

### 314

```python
def f314(rows, keep, prices):
    rows = list(rows)
    selected = []
    totals = {}
    grand = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * abs(prices[group])
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            grand += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(dict.fromkeys(selected)), 'total': grand, 'groups': totals, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f314([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 315

```python
def f315(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:
            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
```

```
f315([('AN', 2), ('BR', 4), ('CX', 9), ('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)], [('BR', 8), ('CX', 4), ('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)], 8)
```

```
{"count":6,"items":[["DL",62],["CX",44],["BR",40],["GQ",38],["EV",28]],"missing":["AN","HR"],"total":240}
```

### 316

```python
def f316(rows, keep, ratemap):
    rows = list(rows)
    matches = []
    groupmap = {}
    amount = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep}:
            charge = value * abs(ratemap[group])
            matches.append((code, charge))
            groupmap[group] = groupmap.get(group, 0) + charge
            amount += charge
    matches.sort(key=lambda item: (-item[1], str(item[0]).casefold()))
    returnvalue = {'accepted': len(matches), 'total': amount, 'groups': groupmap, 'top': [code for code, charge in matches[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f316([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 317

```python
def f317(rows, keep, ratemap):
    rows = list(rows)
    selected = []
    totals = {}
    sumvalue = 0
    for code, group, state, value in rows:
        if str(state).lower() in {str(item).lower() for item in keep} and value >= 0:
            cost = value * ratemap[group]
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            sumvalue += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': sumvalue, 'groups': totals, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f317([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 12, 'edge': 3})
```

```
{"accepted":6,"groups":{"core":480,"edge":72,"south":105},"top":["BR72","BR46","CX20"],"total":657}
```

### 318

```python
def f318(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 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
```

```
f318([('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E'), ('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')], 'A', 2)
```

```
{"count":6,"depth":{"A":0,"B":1,"C":1,"D":2,"E":2,"F":2},"frontier":["D","E","F"],"order":["A","B","C","D","E","F"]}
```

### 319

```python
def f319(rows, keep, factors):
    rows = list(rows)
    selected = []
    totals = {}
    amount = 0
    for code, group, state, value in rows:
        if state in keep:
            cost = value * abs(factors[group])
            selected.append((code, cost))
            totals[group] = totals.get(group, 0) + cost
            amount += cost
    selected.sort(key=lambda item: (-item[1], item[0]))
    returnvalue = {'accepted': len(selected), 'total': amount, 'groups': totals, 'top': [code for code, cost in selected[:3]]}
    output = dict()
    output.update(returnvalue)
    return output
```

```
f319([('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5), ('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)], ['ready', 'checked'], {'north': 7, 'south': 5, 'core': 11, 'edge': 5})
```

```
{"accepted":6,"groups":{"core":440,"edge":120,"south":105},"top":["BR72","BR46","CX61"],"total":665}
```

### 320

```python
def f320(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)
    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
```

```
f320([(3, 5), (6, 10), (15, 17), (20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63)], 2)
```

```
{"cover":33,"holes":[5,3,4,8,3,4],"longest":7,"segments":[[3,10],[15,17],[20,25],[29,36],[44,46],[49,56],[60,63]]}
```

### Final Query

Give me the output of the final query without executing it!

```python
import json, re
from collections import deque
out = {}
lines = list(('Helium, amber. helium helium', 'Helium, frost. frost helium cyan', 'Garnet, frost. cyan cyan') + ('Delta, garnet. ember amber delta', 'Amber, frost. ember amber', 'Ember, blue. garnet cyan ember', 'Amber, cyan. blue helium vivid'))
stop = ['garnet']
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))}
stamp = record['dd']
gap = 2
route = stamp
cases = {
    144: list(((3, 5), (6, 10), (15, 17)) + ((20, 25), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63))),
    145: list(((3, 5), (8, 12), (15, 17)) + ((19, 24), (29, 36), (34, 36), (44, 46), (49, 56), (60, 63))),
}
spans = 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))}
ticket = record['cc']
rows = list((('DL76', 'edge', 'void', 17), ('CX13', 'edge', 'void', 14), ('BR50', 'north', 'void', 20), ('AN87', 'north', 'hold', 12), ('BR24', 'north', 'hold', 18), ('CX61', 'edge', 'ready', 19), ('BR98', 'north', 'void', 9), ('AN35', 'edge', 'ready', 5)) + (('BR72', 'core', 'ready', 23), ('DL09', 'edge', 'void', 23), ('BR46', 'core', 'ready', 17), ('AN83', 'core', 'void', 16), ('CX20', 'south', 'checked', 17), ('AN57', 'south', 'checked', 4)))
keep = list(('ready',) + ('checked',))
route = stamp
cases = {
    145: dict((('north', 7), ('south', 5), ('core', 12)) + (('edge', 3),)),
    144: dict((('north', 7), ('south', 5), ('core', 11)) + (('edge', 5),)),
}
rates = cases[route]
chosen = [(code, group, value) for code, group, state, value in rows if state in keep]
priced = [(code, group, value * rates[group]) for code, group, value in chosen]
groups = {}
for code, group, price in priced:
    groups[group] = groups.get(group, 0) + price
ranked = sorted(priced, key=lambda row: (-row[2], row[0]))
record = {'aa': [row[0] for row in ranked[:3]], 'bb': sum((row[2] for row in priced)), 'cc': len(priced), 'dd': groups}
badge = record['bb']
width = 4
route = (ticket, badge)
cases = {
    (33, 665): (list((17, 4, 21, 24, 14, 18, 11) + (12, 7, 7, 17, 19, 12, 6, 21)), 82),
    (33, 657): (list((17, 4, 21, 24, 17, 18, 11) + (12, 7, 7, 13, 19, 12, 6, 21)), 83),
    (34, 665): (list((17, 4, 21, 24, 17, 18, 11) + (12, 7, 7, 13, 19, 12, 6, 21)), 83),
    (34, 657): (list((17, 4, 21, 24, 17, 18, 11) + (12, 7, 7, 13, 19, 12, 6, 21)), 83),
}
values, limit = cases[route]
current = sum(values[:width])
sums = [current]
for pos in range(width, len(values)):
    current += values[pos] - values[pos - width]
    sums.append(current)
hits = []
rises = 0
for pos, value in enumerate(sums):
    if value >= limit:
        hits.append(pos)
    if pos and value > sums[pos - 1]:
        rises += 1
record = {'aa': hits, 'bb': max(sums), 'cc': rises, 'dd': sums}
permit = record['bb']
route = permit
cases = {
    80: list((('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2)) + (('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('S', 2))),
    77: list((('W', 1), ('E', 3), ('N', 1), ('S', 2), ('E', 1), ('E', 3), ('W', 2)) + (('E', 2), ('W', 3), ('W', 1), ('N', 1), ('E', 1), ('N', 2), ('N', 2), ('E', 2), ('W', 1))),
}
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}
signal = record['ee']
nodes = list(('cache', 'ui', 'proxy', 'auth', 'api') + ('worker', 'jobs', 'db'))
route = signal
cases = {
    28: list((('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs')) + (('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('auth', 'db'))),
    29: list((('auth', 'api'), ('db', 'api'), ('cache', 'api'), ('api', 'ui'), ('db', 'jobs')) + (('jobs', 'worker'), ('auth', 'proxy'), ('proxy', 'ui'), ('db', 'auth'))),
}
edges = cases[route]
remaining = set(nodes)
done = set()
order = []
batches = []
while remaining:
    ready = sorted((node for node in remaining if all((before in done for before, after in edges if after == node))))
    if not ready:
        break
    batches.append(ready)
    order.extend(ready)
    done.update(ready)
    remaining.difference_update(ready)
roots = sorted((node for node in nodes if all((after != node for before, after in edges))))
record = {'aa': order, 'bb': batches, 'cc': roots, 'dd': len(order)}
token = record['aa'][0]
edges = list((('A', 'C'), ('A', 'B'), ('B', 'D'), ('B', 'E')) + (('C', 'F'), ('D', 'G'), ('E', 'G'), ('F', 'H'), ('G', 'A')))
start = 'A'
route = token
cases = {
    'cache': 2,
    'auth': 4,
}
limit = 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)}
memo = record['dd']
left = list((('AN', 2), ('BR', 4), ('CX', 9)) + (('DL', 9), ('EV', 2), ('FP', 5), ('GQ', 5), ('HR', 2)))
right = list((('BR', 8), ('CX', 4)) + (('DL', 6), ('EV', 10), ('FP', 4), ('GQ', 6)))
route = memo
cases = {
    8: 8,
    6: 2,
}
fee = 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['bb'] = record['bb']
out['cc'] = record['cc']
out['dd'] = record['dd']
print(json.dumps(out, separators=(",", ":"), sort_keys=True))
```