



class     _A       :



       def __init__(		self							:     Any     ,		__SCREAMING_SNAKE_CASE							:     int):


           '''simple docstring'''

           __a						       =				n
           __a						       =				[None] * self.n
           __a						       =				0  # index of the first element
           __a						       =				0
           __a						       =				0



       def __len__(		self							:     str):


           '''simple docstring'''

           return self.size



       def 		_lowerCamelCase			(		self							:     int):


           '''simple docstring'''

           return self.size == 0



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           return False if self.is_empty() else self.array[self.front]



       def 		_lowerCamelCase			(		self							:     str     ,		__SCREAMING_SNAKE_CASE							:     Optional[Any]):


           '''simple docstring'''

           if self.size >= self.n:
               raise Exception('''QUEUE IS FULL''')

           __a						       =				data
           __a						       =				(self.rear + 1) % self.n
           self.size += 1
           return self





       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           if self.size == 0:
               raise Exception('''UNDERFLOW''')

           __a						       =				self.array[self.front]
           __a						       =				None
           __a						       =				(self.front + 1) % self.n
           self.size -= 1
           return temp






"""simple docstring"""






from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 				snake_case       :




					"""simple docstring"""

					snake_case__				    = 42
					snake_case__				    = None
					snake_case__				    = None






lowerCAmelCase__  :  Union[str, Any]						     =	namedtuple('CoinsDistribResult', 'moves excess')



def   a_						(					lowerCamelCase       ):

				if root is None:
								return 0

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

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

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

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

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

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

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

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

								UpperCAmelCase__             =							1 - left_distrib_excess
								UpperCAmelCase__             =							1 - right_distrib_excess

								UpperCAmelCase__             =							(
								    left_distrib_moves
								    + right_distrib_moves
								    + abs(lowerCamelCase       )
								    + abs(lowerCamelCase       )
								)
								UpperCAmelCase__             =							node.data - coins_to_left - coins_to_right

								return CoinsDistribResult(lowerCamelCase					,			lowerCamelCase       )

				return get_distrib(lowerCamelCase       )[0]


if __name__ == "__main__":
						import doctest

						doctest.testmod()



