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Merged
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Oct 13, 2019
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Add safe_cracker to ch07 #13

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JoseALermaIII Oct 13, 2019
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Add compare
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Initialize TestSafeCracker with test_compare
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Add crack_safe
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Add setUpClass to TestSafeCracker
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Add test_crack_safe to TestSafeCracker
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Add c2_safe_cracker
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[skip ci] Reword compare docstring
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Reword compare docstring
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Merge remote-tracking branch 'origin/safe-cracker' into safe-cracker
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8 changes: 8 additions & 0 deletions docs/source/src.ch07.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,14 @@ src.ch07.c1\_breed\_rats module
:undoc-members:
:show-inheritance:

src.ch07.c2\_safe\_cracker module
---------------------------------

.. automodule:: src.ch07.c2_safe_cracker
:members:
:undoc-members:
:show-inheritance:


Module contents
---------------
Expand Down
99 changes: 99 additions & 0 deletions src/ch07/c2_safe_cracker.py
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"""Use hill-climbing algorithm to solve a lock combination.

Solve a lock combination by randomly changing a tumbler's values one
by one and noting whether the safe had a response. If so, lock the
tumbler at that value and continue randomly changing tumbler values.

Previously, a locked tumbler can still be changed, but the safe wouldn't
respond, so the change would be discarded. This improves upon the algorithm by
removing the locked tumbler from the pool of tumblers to randomly change.

"""
import time
import random


def compare(combo: list, attempt: list) -> int:
"""Compare items in two lists and count number of matches.

Compare each tumbler in **combo** with **attempt** and return
the number of matches.

Args:
combo (list): Integers of safe combination.
attempt (list): Integers of guessed safe combination.

Returns:
Number of tumbler matches between **combo** and **attempt**.

"""
return sum(1 for i, j in zip(combo, attempt) if i == j)


def crack_safe(combo: str) -> tuple:
"""Crack a safe combination with a hill-climbing algorithm.

Solve a lock combination by randomly changing a tumbler's values one
by one and noting whether the safe had a response. If so, lock the
tumbler at that value, remove it from the pool of tumblers, and
continue randomly changing tumbler values.

Args:
combo (str): String of numbers representing combination of safe.

Returns:
Tuple with string of solved combination and number of attempts.

"""
# Convert combo to list.
combo = [int(i) for i in combo]

# Make initial guess and compare.
best_guess = [0] * len(combo)
best_guess_match = compare(combo, best_guess)

count = 0
tumblers = list(range(len(combo)))

# Evolve guess.
while best_guess != combo:
# Crossover.
guess = best_guess.copy()

# Mutate.
lock_tumbler = random.choice(tumblers)
guess[lock_tumbler] = random.randint(0, len(combo) - 1)

# Compare and select.
guess_match = compare(combo, guess)
if guess_match > best_guess_match:
best_guess = guess.copy()
best_guess_match = guess_match
tumblers.remove(lock_tumbler)
print(guess, best_guess)
count += 1
return ''.join([str(i) for i in best_guess]), count


def main():
"""Demonstrate safe cracker.

Use default combination to demonstrate :func:`crack_safe` and display time
(in seconds) it took to run.

"""
start_time = time.time()

combination = '6822858902'
print(f'Combination: {combination}')
guess, count = crack_safe(combination)
print(f'\nCracked! {guess} ')
print(f'in {count} tries!')

end_time = time.time()
duration = end_time - start_time
print(f'\nRuntime for this program was {duration:.5f} seconds.')


if __name__ == '__main__':
main()
127 changes: 127 additions & 0 deletions tests/data/ch07/main/safe_cracker.txt
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Combination: 6822858902
[0, 0, 0, 5, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 3, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 6, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 6, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 3, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 7, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 6, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 6, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 5, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 3, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 0, 6, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 6, 0, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 1, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 7, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 5, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 8, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 0, 0, 7, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 8, 0, 7, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 9, 0, 0, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 7, 0, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 0, 0, 0, 0, 8, 0, 8, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[5, 0, 0, 0, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 0, 7, 0, 0, 8, 0, 0, 2] [0, 0, 0, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 0, 0, 2] [0, 0, 2, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 2, 0, 0, 8, 8, 0, 0, 2] [0, 0, 2, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 2, 0, 9, 0, 8, 0, 0, 2] [0, 0, 2, 0, 0, 0, 8, 0, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 9, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 3, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 2, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 9, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 4, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 1, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 1, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 5, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 3, 2, 0, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 9, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 1, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 6, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 3, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 0, 0, 0, 8, 9, 1, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[0, 0, 2, 4, 0, 0, 8, 9, 0, 2] [0, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 0, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 3, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 7, 2, 0, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 0, 0, 4, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 0, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 3, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 0, 0, 9, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 0, 2, 0, 0, 0, 8, 9, 0, 2] [6, 0, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 0, 8, 9, 0, 2] [6, 8, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 4, 8, 9, 0, 2] [6, 8, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 3, 8, 9, 0, 2] [6, 8, 2, 0, 0, 0, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 6, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 4, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 8, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 6, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 9, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 5, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 6, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 6, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 8, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 9, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 4, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 3, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 7, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 1, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 9, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 4, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 9, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 3, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 5, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 2, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 4, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 8, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 1, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 9, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 5, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 4, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 4, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 1, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 0, 5, 8, 9, 0, 2] [6, 8, 2, 0, 0, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 3, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 8, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 9, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 4, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 8, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 6, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 3, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 4, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 6, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 6, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 8, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 7, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 8, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 7, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 7, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 3, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 7, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 7, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 7, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 4, 8, 5, 8, 9, 0, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 4, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 6, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 0, 8, 5, 8, 9, 6, 2] [6, 8, 2, 0, 8, 5, 8, 9, 0, 2]
[6, 8, 2, 2, 8, 5, 8, 9, 0, 2] [6, 8, 2, 2, 8, 5, 8, 9, 0, 2]

Cracked! 6822858902
in 121 tries!

Runtime for this program was 55545.00000 seconds.
110 changes: 110 additions & 0 deletions tests/data/ch07/safe_cracker.txt
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Original file line number Diff line number Diff line change
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 5] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 8, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 5] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 9] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 6, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 9, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 2] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 2, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 3, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 8, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 7, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 9, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 2, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 8, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 5, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 6, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 6, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 4, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 8, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 9, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 4, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 8, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 5, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 0, 3, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 4, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 5, 4, 0, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 0, 6, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 7, 0, 4, 0, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 9, 0, 0, 0, 0, 0] [0, 0, 0, 4, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 1, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 0, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 6, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 8, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 3, 0, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 9, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 1, 0, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[0, 0, 0, 4, 0, 0, 0, 0, 0, 3] [0, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 0, 0, 0, 0, 3] [8, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 0, 0, 3, 0, 3] [8, 0, 0, 4, 0, 0, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 4, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 4, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 2, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 3, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 8, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 2, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 8, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 8, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 5, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 9, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 8, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 0, 0, 8, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 2, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 6, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 4, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 4, 0, 4, 0, 9, 0, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 0, 4, 0, 9, 9, 0, 0, 3] [8, 0, 0, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 0, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 0, 7, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 2, 9, 0, 0, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 0, 7, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 9, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 2, 0, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 0, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 4, 0, 0, 3] [8, 0, 7, 4, 0, 9, 0, 0, 0, 3]
[8, 0, 7, 4, 0, 9, 0, 2, 0, 3] [8, 0, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 2, 7, 4, 0, 9, 0, 2, 0, 3] [8, 0, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 4, 7, 4, 0, 9, 0, 2, 0, 3] [8, 0, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 0, 7, 4, 0, 9, 8, 2, 0, 3] [8, 0, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 2, 7, 4, 0, 9, 0, 2, 0, 3] [8, 0, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 7, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 7, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 2, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 7, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 3, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 4, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 3, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 7, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 6, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 7, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 9, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 3, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 3, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 8, 9, 0, 2, 0, 3] [8, 9, 7, 4, 0, 9, 0, 2, 0, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 9, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 0, 9, 9, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 0, 9, 5, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 3, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 7, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 4, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 0, 9, 6, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 0, 9, 0, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 0, 9, 4, 2, 1, 3] [8, 9, 7, 4, 0, 9, 0, 2, 1, 3]
[8, 9, 7, 4, 5, 9, 0, 2, 1, 3] [8, 9, 7, 4, 5, 9, 0, 2, 1, 3]
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