
from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass






@dataclass
class   UpperCAmelCase		:
   A__					:		int
   A__					:		TreeNode | None						     =     None
   A__					:		TreeNode | None						     =     None



__lowerCamelCase							=       namedtuple("""CoinsDistribResult""", """moves excess""")


def 			UpperCamelCase					(    __lowerCamelCase     : TreeNode | None    ):

       if root is None:
              return 0

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

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

       def count_coins(__lowerCamelCase     : TreeNode | None    ) -> int:
              if node is None:
                     return 0

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

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

       # Main calculation
       def get_distrib(__lowerCamelCase     : TreeNode | None    ) -> CoinsDistribResult:

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

              snake_case				,					snake_case       :   List[str]							=      get_distrib(node.left    )
              snake_case				,					snake_case       :   List[str]							=      get_distrib(node.right    )

              snake_case       :   List[str]							=      1 - left_distrib_excess
              snake_case       :   int							=      1 - right_distrib_excess

              snake_case       :   List[str]							=      (
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(__lowerCamelCase    )
                  + abs(__lowerCamelCase    )
              )
              snake_case       :   Tuple							=      node.data - coins_to_left - coins_to_right

              return CoinsDistribResult(__lowerCamelCase				,					__lowerCamelCase    )

       return get_distrib(__lowerCamelCase    )[0]


if __name__ == "__main__":
   import doctest

   doctest.testmod()









"""simple docstring"""




def     lowercase			(SCREAMING_SNAKE_CASE_		:				int  )   ->						str:
						SCREAMING_SNAKE_CASE													=					int(SCREAMING_SNAKE_CASE_  )
						if decimal in (0, 1):  # Exit cases for the recursion
												return str(SCREAMING_SNAKE_CASE_  )
						SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE													=					divmod(SCREAMING_SNAKE_CASE_ ,			2  )
						return binary_recursive(SCREAMING_SNAKE_CASE_  ) + str(SCREAMING_SNAKE_CASE_  )


def     lowercase			(SCREAMING_SNAKE_CASE_		:				str  )   ->						str:
						SCREAMING_SNAKE_CASE													=					str(SCREAMING_SNAKE_CASE_  ).strip()
						if not number:
												raise ValueError('No input value was provided'  )
						SCREAMING_SNAKE_CASE													=					'-' if number.startswith('-'  ) else ''
						SCREAMING_SNAKE_CASE													=					number.lstrip('-'  )
						if not number.isnumeric():
												raise ValueError('Input value is not an integer'  )
						return F'{negative}0b{binary_recursive(int(SCREAMING_SNAKE_CASE_  )  )}'


if __name__ == "__main__":
	from doctest import testmod

	testmod()


