



from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 				_snake_case			:
				UpperCamelCase__				:					int
				UpperCamelCase__				:					TreeNode | None     		=None
				UpperCamelCase__				:					TreeNode | None     		=None
lowercase_								=     namedtuple("""CoinsDistribResult""", """moves excess""")



def __lowerCAmelCase (     SCREAMING_SNAKE_CASE_  ):

			if root is None:
						return 0

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

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

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

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

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

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

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

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

						lowercase__					  =				1 - left_distrib_excess
						lowercase__					  =				1 - right_distrib_excess

						lowercase__					  =				(
						    left_distrib_moves
						    + right_distrib_moves
						    + abs(SCREAMING_SNAKE_CASE_  )
						    + abs(SCREAMING_SNAKE_CASE_  )
						)
						lowercase__					  =				node.data - coins_to_left - coins_to_right

						return CoinsDistribResult(SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_  )

			return get_distrib(SCREAMING_SNAKE_CASE_  )[0]


if __name__ == "__main__":
							import doctest

							doctest.testmod()









def __lowerCAmelCase (     SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_  ):
			lowercase__  ,       lowercase__					  =				len(SCREAMING_SNAKE_CASE_  ), len(grid[0]  )
			if (
			    min(SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_  ) < 0
			    or row == row_length
			    or col == col_length
			    or (row, col) in visit
			    or grid[row][col] == 1
			):
						return 0
			if row == row_length - 1 and col == col_length - 1:
						return 1

			visit.add((row, col)  )

			lowercase__					  =				0
			count += depth_first_search(SCREAMING_SNAKE_CASE_						,  row + 1						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_  )
			count += depth_first_search(SCREAMING_SNAKE_CASE_						,  row - 1						,  SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_  )
			count += depth_first_search(SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  col + 1						,  SCREAMING_SNAKE_CASE_  )
			count += depth_first_search(SCREAMING_SNAKE_CASE_						,  SCREAMING_SNAKE_CASE_						,  col - 1						,  SCREAMING_SNAKE_CASE_  )

			visit.remove((row, col)  )
			return count


if __name__ == "__main__":
							import doctest

							doctest.testmod()




