"""simple docstring"""






# This is the module that test_patching.py uses to test patch_submodule()

import os  # noqa: this is just for tests
import os as renamed_os  # noqa: this is just for tests
from os import path  # noqa: this is just for tests
from os import path as renamed_path  # noqa: this is just for tests
from os.path import join  # noqa: this is just for tests
from os.path import join as renamed_join  # noqa: this is just for tests


lowerCAmelCase__  :  List[str]						     =	open  # noqa: we just need to have a builtin inside this module to test it properly




"""simple docstring"""






from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 				snake_case       :




					"""simple docstring"""

					snake_case__				    = 42
					snake_case__				    = None
					snake_case__				    = None






lowerCAmelCase__  :  Union[str, Any]						     =	namedtuple('CoinsDistribResult', 'moves excess')



def   a_						(					lowerCamelCase       ):

				if root is None:
								return 0

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

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

				def count_coins(lowerCamelCase       ) -> 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       ) -> CoinsDistribResult:

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

								UpperCAmelCase__      ,	UpperCAmelCase__             =							get_distrib(node.left       )
								UpperCAmelCase__      ,	UpperCAmelCase__             =							get_distrib(node.right       )

								UpperCAmelCase__             =							1 - left_distrib_excess
								UpperCAmelCase__             =							1 - right_distrib_excess

								UpperCAmelCase__             =							(
								    left_distrib_moves
								    + right_distrib_moves
								    + abs(lowerCamelCase       )
								    + abs(lowerCamelCase       )
								)
								UpperCAmelCase__             =							node.data - coins_to_left - coins_to_right

								return CoinsDistribResult(lowerCamelCase					,			lowerCamelCase       )

				return get_distrib(lowerCamelCase       )[0]


if __name__ == "__main__":
						import doctest

						doctest.testmod()



