



from heapq import heappop, heappush

import numpy as np



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	):
	__lowercase		       =			grid.shape
	__lowercase		       =			[-1, 1, 0, 0]
	__lowercase		       =			[0, 0, -1, 1]
	if allow_diagonal:
		dx += [-1, -1, 1, 1]
		dy += [-1, 1, -1, 1]

	__lowercase		       =			[(0, source)], set()
	__lowercase		       =			np.full((rows, cols)  ,	np.inf   )
	__lowercase		       =			0
	__lowercase		       =			np.empty((rows, cols)  ,	dtype=_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			None

	while queue:
		(__lowercase)		       =			heappop(_SCREAMING_SNAKE_CASE   )
		if (x, y) in visited:
			continue
		visited.add((x, y)   )

		if (x, y) == destination:
			__lowercase		       =			[]
			while (x, y) != source:
				path.append((x, y)   )
				__lowercase		       =			predecessors[x, y]
			path.append(_SCREAMING_SNAKE_CASE   )  # add the source manually
			path.reverse()
			return matrix[destination], path

		for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
			__lowercase		       =			x + dx[i], y + dy[i]
			if 0 <= nx < rows and 0 <= ny < cols:
				__lowercase		       =			grid[nx][ny]
				if next_node == 1 and matrix[nx, ny] > dist + 1:
					heappush(_SCREAMING_SNAKE_CASE  ,	(dist + 1, (nx, ny))   )
					__lowercase		       =			dist + 1
					__lowercase		       =			(x, y)

	return np.inf, []


if __name__ == "__main__":
	import doctest

	doctest.testmod()








from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass

@dataclass
class   _A   :


						'''simple docstring'''





						_snake_case			:     int
						_snake_case			:     TreeNode | None      							=      None
						_snake_case			:     TreeNode | None      							=      None

snake_case__					:     Dict    		=   namedtuple("""CoinsDistribResult""", """moves excess""")



def    snake_case_				(    _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()



