


from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass




@dataclass
class        lowerCamelCase      :
	_lowerCAmelCase    :		int
	_lowerCAmelCase    :		TreeNode | None        =	None
	_lowerCAmelCase    :		TreeNode | None        =	None






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




def 						__SCREAMING_SNAKE_CASE       (					lowercase_			)		->    int:




						'''simple docstring'''







						if root is None:
												return 0

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

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

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

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

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

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

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

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

												__UpperCAmelCase :       Optional[Any]  						=  1 - left_distrib_excess
												__UpperCAmelCase :       Union[str, Any]  						=  1 - right_distrib_excess

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

												return CoinsDistribResult(lowercase_			,					lowercase_			)

						return get_distrib(lowercase_			)[0]


if __name__ == "__main__":
				import doctest

				doctest.testmod()





from __future__ import annotations




def 						__SCREAMING_SNAKE_CASE       (					lowercase_			)		->    int:




						'''simple docstring'''







						if not nums:
												return 0
						__UpperCAmelCase :       int  						=  nums[0]
						__UpperCAmelCase :       Optional[Any]  						=  0
						for num in nums[1:]:
												__UpperCAmelCase						,			__UpperCAmelCase :       int  						=  (
												    max_excluding + num,
												    max(lowercase_			,					lowercase_			),
												)
						return max(lowercase_			,					lowercase_			)


if __name__ == "__main__":
				import doctest

				doctest.testmod()

