






import functools
from typing import Any



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      str      ,					__lowercase :      list[str]     )    ->   bool:





    """simple docstring"""

    if not isinstance(__lowercase      ,					__lowercase     ) or len(__lowercase     ) == 0:
        raise ValueError("""the string should be not empty string"""     )

    if not isinstance(__lowercase      ,					__lowercase     ) or not all(
        isinstance(__lowercase      ,					__lowercase     ) and len(__lowercase     ) > 0 for item in words     ):
        raise ValueError("""the words should be a list of non-empty strings"""     )

    # Build trie
    __A       =						{}
    __A       =						"""WORD_KEEPER"""

    for word in words:
        __A       =						trie
        for c in word:
            if c not in trie_node:
                __A       =						{}

            __A       =						trie_node[c]

        __A       =						True

    __A       =						len(__lowercase     )

    # Dynamic programming method
    @functools.cache
    def is_breakable(__lowercase :      int     ) -> bool:
        if index == len_string:
            return True

        __A       =						trie
        for i in range(__lowercase      ,					__lowercase     ):
            __A       =						trie_node.get(string[i]      ,					__lowercase     )

            if trie_node is None:
                return False

            if trie_node.get(__lowercase      ,					__lowercase     ) and is_breakable(i + 1     ):
                return True

        return False

    return is_breakable(0     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()












from __future__ import annotations

from PIL import Image

# Define glider example
__a   :							Tuple						= [
    [0, 1, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0, 0],
    [1, 1, 1, 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, 0, 0, 0],
]

# Define blinker example
__a   :							Optional[Any]						= [[0, 1, 0], [0, 1, 0], [0, 1, 0]]



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      list[list[int]]     )    ->   list[list[int]]:





    """simple docstring"""

    __A       =						[]
    for i in range(len(__lowercase     )     ):
        __A       =						[]
        for j in range(len(cells[i]     )     ):
            # Get the number of live neighbours
            __A       =						0
            if i > 0 and j > 0:
                neighbour_count += cells[i - 1][j - 1]
            if i > 0:
                neighbour_count += cells[i - 1][j]
            if i > 0 and j < len(cells[i]     ) - 1:
                neighbour_count += cells[i - 1][j + 1]
            if j > 0:
                neighbour_count += cells[i][j - 1]
            if j < len(cells[i]     ) - 1:
                neighbour_count += cells[i][j + 1]
            if i < len(__lowercase     ) - 1 and j > 0:
                neighbour_count += cells[i + 1][j - 1]
            if i < len(__lowercase     ) - 1:
                neighbour_count += cells[i + 1][j]
            if i < len(__lowercase     ) - 1 and j < len(cells[i]     ) - 1:
                neighbour_count += cells[i + 1][j + 1]

            # Rules of the game of life (excerpt from Wikipedia):
            # 1. Any live cell with two or three live neighbours survives.
            # 2. Any dead cell with three live neighbours becomes a live cell.
            # 3. All other live cells die in the next generation.
            #    Similarly, all other dead cells stay dead.
            __A       =						cells[i][j] == 1
            if (
                (alive and 2 <= neighbour_count <= 3)
                or not alive
                and neighbour_count == 3
            ):
                next_generation_row.append(1     )
            else:
                next_generation_row.append(0     )

        next_generation.append(__lowercase     )
    return next_generation



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      list[list[int]]      ,					__lowercase :      int     )    ->   list[Image.Image]:





    """simple docstring"""

    __A       =						[]
    for _ in range(__lowercase     ):
        # Create output image
        __A       =						Image.new("""RGB"""      ,					(len(cells[0]     ), len(__lowercase     ))     )
        __A       =						img.load()

        # Save cells to image
        for x in range(len(__lowercase     )     ):
            for y in range(len(cells[0]     )     ):
                __A       =						2_5_5 - cells[y][x] * 2_5_5
                __A       =						(colour, colour, colour)

        # Save image
        images.append(__lowercase     )
        __A       =						new_generation(__lowercase     )
    return images


if __name__ == "__main__":
  __a   :							Optional[int]						= generate_images(GLIDER, 16)
  images[0].save("out.gif", save_all=True, append_images=images[1:])




