



'''simple docstring'''





from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass






@dataclass
class        lowerCAmelCase_:
  '''simple docstring'''




  __lowercase							:      int
  __lowercase							:      TreeNode | None				=      None
  __lowercase							:      TreeNode | None				=      None







_lowerCAmelCase      						=	namedtuple('''CoinsDistribResult''', '''moves excess''')
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    if root is None:
        return 0

    # Validation
    def count_nodes(UpperCamelCase			) -> int:
        if node is None:
            return 0

        return count_nodes(node.left			) + count_nodes(node.right			) + 1

    def count_coins(UpperCamelCase			) -> int:
        if node is None:
            return 0

        return count_coins(node.left			) + count_coins(node.right			) + node.data

    if count_nodes(UpperCamelCase			) != count_coins(UpperCamelCase			):
        raise ValueError("""The nodes number should be same as the number of coins"""			)

    # Main calculation
    def get_distrib(UpperCamelCase			) -> CoinsDistribResult:

        if node is None:
            return CoinsDistribResult(0							,    1			)

        lowerCAmelCase__      ,   lowerCAmelCase__ :  List[Any]							      =					get_distrib(node.left			)
        lowerCAmelCase__      ,   lowerCAmelCase__ :  Union[str, Any]							      =					get_distrib(node.right			)

        lowerCAmelCase__ :  Optional[int]							      =					1 - left_distrib_excess
        lowerCAmelCase__ :  Dict							      =					1 - right_distrib_excess

        lowerCAmelCase__ :  Union[str, Any]							      =					(
            left_distrib_moves
            + right_distrib_moves
            + abs(UpperCamelCase			)
            + abs(UpperCamelCase			)
        )
        lowerCAmelCase__ :  Union[str, Any]							      =					node.data - coins_to_left - coins_to_right

        return CoinsDistribResult(UpperCamelCase							,    UpperCamelCase			)

    return get_distrib(UpperCamelCase			)[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




def 			UpperCamelCase					(    __lowerCamelCase     : str				,					__lowerCamelCase     : int    ):
       snake_case       :   list[list[str]]							=      [[] for _ in range(__lowerCamelCase    )]
       snake_case       :   int							=      key - 1

       if key <= 0:
              raise ValueError("Height of grid can't be 0 or negative"    )
       if key == 1 or len(__lowerCamelCase    ) <= key:
              return input_string

       for position, character in enumerate(__lowerCamelCase    ):
              snake_case       :   Any							=      position % (lowest * 2)  # puts it in bounds
              snake_case       :   Optional[int]							=      min(__lowerCamelCase				,					lowest * 2 - num    )  # creates zigzag pattern
              temp_grid[num].append(__lowerCamelCase    )
       snake_case       :   List[str]							=      ["".join(__lowerCamelCase    ) for row in temp_grid]
       snake_case       :   Tuple							=      "".join(__lowerCamelCase    )

       return output_string


def 			UpperCamelCase					(    __lowerCamelCase     : str				,					__lowerCamelCase     : int    ):
       snake_case       :   Dict							=      []
       snake_case       :   Union[str, Any]							=      key - 1

       if key <= 0:
              raise ValueError("Height of grid can't be 0 or negative"    )
       if key == 1:
              return input_string

       snake_case       :   list[list[str]]							=      [[] for _ in range(__lowerCamelCase    )]  # generates template
       for position in range(len(__lowerCamelCase    )    ):
              snake_case       :   List[str]							=      position % (lowest * 2)  # puts it in bounds
              snake_case       :   Optional[int]							=      min(__lowerCamelCase				,					lowest * 2 - num    )  # creates zigzag pattern
              temp_grid[num].append("*"    )

       snake_case       :   Tuple							=      0
       for row in temp_grid:  # fills in the characters
              snake_case       :   Union[str, Any]							=      input_string[counter : counter + len(__lowerCamelCase    )]
              grid.append(list(__lowerCamelCase    )    )
              counter += len(__lowerCamelCase    )

       snake_case       :   str							=      ""  # reads as zigzag
       for position in range(len(__lowerCamelCase    )    ):
              snake_case       :   Optional[int]							=      position % (lowest * 2)  # puts it in bounds
              snake_case       :   Tuple							=      min(__lowerCamelCase				,					lowest * 2 - num    )  # creates zigzag pattern
              output_string += grid[num][0]
              grid[num].pop(0    )
       return output_string


def 			UpperCamelCase					(    __lowerCamelCase     : str    ):
       snake_case       :   Tuple							=      {}
       for key_guess in range(1				,					len(__lowerCamelCase    )    ):  # tries every key
              snake_case       :   Any							=      decrypt(__lowerCamelCase				,					__lowerCamelCase    )
       return results


if __name__ == "__main__":
   import doctest

   doctest.testmod()





