

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		:   int										=       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()







from __future__ import annotations

import numpy as np





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_				,    snake_case_							=    np.shape(UpperCamelCase__      )
							if rows != columns:
														snake_case_							=    (
														    '\'table\' has to be of square shaped array but got a '
														    F'''{rows}x{columns} array:\n{table}'''
														)
														raise ValueError(UpperCamelCase__      )

							snake_case_							=    np.zeros((rows, columns)      )
							snake_case_							=    np.zeros((rows, columns)      )
							for i in range(UpperCamelCase__      ):
														for j in range(UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					if upper[j][j] == 0:
																												raise ArithmeticError('No LU decomposition exists'      )
																					snake_case_							=    (table[i][j] - total) / upper[j][j]
														snake_case_							=    1
														for j in range(UpperCamelCase__   ,							UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					snake_case_							=    table[i][j] - total
							return lower, upper


if __name__ == "__main__":
					import doctest

					doctest.testmod()




