

from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass







@dataclass
class 				lowercase       :
				__SCREAMING_SNAKE_CASE      :				int
				__SCREAMING_SNAKE_CASE      :				TreeNode | None     =    None
				__SCREAMING_SNAKE_CASE      :				TreeNode | None     =    None



_UpperCAmelCase	:     List[str]		       = namedtuple("""CoinsDistribResult""", """moves excess""")





def       __lowerCamelCase			(				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   )

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

														snake_case_           =					1 - left_distrib_excess
														snake_case_           =					1 - right_distrib_excess

														snake_case_           =					(
														    left_distrib_moves
														    + right_distrib_moves
														    + abs(UpperCamelCase__   )
														    + abs(UpperCamelCase__   )
														)
														snake_case_           =					node.data - coins_to_left - coins_to_right

														return CoinsDistribResult(UpperCamelCase__     ,							UpperCamelCase__   )

							return get_distrib(UpperCamelCase__   )[0]


if __name__ == "__main__":
					import doctest

					doctest.testmod()







_UpperCAmelCase	:     str		       = [0, 2, 4, 6, 8]
_UpperCAmelCase	:     Any		       = [1, 3, 5, 7, 9]





def       __lowerCamelCase			(				UpperCamelCase__     ,							UpperCamelCase__     ,							UpperCamelCase__     ,							UpperCamelCase__   ):







							'''simple docstring'''






							if remaining_length == 0:
														if digits[0] == 0 or digits[-1] == 0:
																					return 0

														for i in range(length // 2 - 1     ,							-1     ,							-1   ):
																					remainder += digits[i] + digits[length - i - 1]

																					if remainder % 2 == 0:
																												return 0

																					remainder //= 10

														return 1

							if remaining_length == 1:
														if remainder % 2 == 0:
																					return 0

														snake_case_           =					0
														for digit in range(10   ):
																					snake_case_           =					digit
																					result += reversible_numbers(
																					    0     ,							(remainder + 2 * digit) // 10     ,							UpperCamelCase__     ,							UpperCamelCase__   )
														return result

							snake_case_           =					0
							for digita in range(10   ):
														snake_case_           =					digita

														if (remainder + digita) % 2 == 0:
																					snake_case_           =					ODD_DIGITS
														else:
																					snake_case_           =					EVEN_DIGITS

														for digita in other_parity_digits:
																					snake_case_           =					digita
																					result += reversible_numbers(
																					    remaining_length - 2     ,							(remainder + digita + digita) // 10     ,							UpperCamelCase__     ,							UpperCamelCase__     ,							)
							return result





def       __lowerCamelCase			(				UpperCamelCase__ = 9   ):







							'''simple docstring'''






							snake_case_           =					0
							for length in range(1     ,							max_power + 1   ):
														result += reversible_numbers(UpperCamelCase__     ,							0     ,							[0] * length     ,							UpperCamelCase__   )
							return result


if __name__ == "__main__":
					print(F'''{solution() = }''')




