


'''simple docstring'''
from __future__ import annotations

from collections.abc import MutableSequence
class   lowercase      :

		"""simple docstring"""

		def __init__(						self       ,  UpperCamelCase_       ,  UpperCamelCase_				):

							'''simple docstring'''


							if len(UpperCamelCase_				) != degree + 1:
												raise ValueError(
												    '''The number of coefficients should be equal to the degree + 1.'''				)

							UpperCamelCase__  :list[float]				   =					list(UpperCamelCase_				)
							UpperCamelCase__  :Tuple				   =					degree




		def __add__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							if self.degree > polynomial_a.degree:
												UpperCamelCase__  :List[str]				   =					self.coefficients[:]
												for i in range(polynomial_a.degree + 1				):
																	coefficients[i] += polynomial_a.coefficients[i]
												return Polynomial(self.degree       ,  UpperCamelCase_				)
							else:
												UpperCamelCase__  :Optional[Any]				   =					polynomial_a.coefficients[:]
												for i in range(self.degree + 1				):
																	coefficients[i] += self.coefficients[i]
												return Polynomial(polynomial_a.degree       ,  UpperCamelCase_				)




		def __sub__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							return self + polynomial_a * Polynomial(0       ,  [-1]				)




		def __neg__(						self				):

							'''simple docstring'''


							return Polynomial(self.degree       ,  [-c for c in self.coefficients]				)




		def __mul__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							UpperCamelCase__  :list[float]				   =					[0] * (self.degree + polynomial_a.degree + 1)
							for i in range(self.degree + 1				):
												for j in range(polynomial_a.degree + 1				):
																	coefficients[i + j] += (
																	    self.coefficients[i] * polynomial_a.coefficients[j]
																	)

							return Polynomial(self.degree + polynomial_a.degree       ,  UpperCamelCase_				)




		def        lowerCAmelCase__							(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							UpperCamelCase__  :int | float				   =					0
							for i in range(self.degree + 1				):
												result += self.coefficients[i] * (substitution**i)
							return result




		def __str__(						self				):

							'''simple docstring'''


							UpperCamelCase__  :int				   =					''''''
							for i in range(self.degree       ,  -1       ,  -1				):
												if self.coefficients[i] == 0:
																	continue
												elif self.coefficients[i] > 0:
																	if polynomial:
																						polynomial += " + "
												else:
																	polynomial += " - "

												if i == 0:
																	polynomial += str(abs(self.coefficients[i]				)				)
												elif i == 1:
																	polynomial += str(abs(self.coefficients[i]				)				) + "x"
												else:
																	polynomial += str(abs(self.coefficients[i]				)				) + "x^" + str(UpperCamelCase_				)

							return polynomial




		def __repr__(						self				):

							'''simple docstring'''


							return self.__str__()




		def        lowerCAmelCase__							(						self				):

							'''simple docstring'''


							UpperCamelCase__  :list[float]				   =					[0] * self.degree
							for i in range(self.degree				):
												UpperCamelCase__  :List[Any]				   =					self.coefficients[i + 1] * (i + 1)
							return Polynomial(self.degree - 1       ,  UpperCamelCase_				)




		def        lowerCAmelCase__							(						self       ,  UpperCamelCase_ = 0				):

							'''simple docstring'''


							UpperCamelCase__  :list[float]				   =					[0] * (self.degree + 2)
							UpperCamelCase__  :Tuple				   =					constant
							for i in range(self.degree + 1				):
												UpperCamelCase__  :Any				   =					self.coefficients[i] / (i + 1)
							return Polynomial(self.degree + 1       ,  UpperCamelCase_				)




		def __eq__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_       ,  UpperCamelCase_				):
												return False

							if self.degree != polynomial_a.degree:
												return False

							for i in range(self.degree + 1				):
												if self.coefficients[i] != polynomial_a.coefficients[i]:
																	return False

							return True




		def __ne__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							return not self.__eq__(UpperCamelCase_				)



'''simple docstring'''
from __future__ import annotations

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

		"""simple docstring"""

		_a       					=							42
		_a       					=							None
		_a       					=							None



__snake_case				 =	namedtuple('''CoinsDistribResult''', '''moves excess''')


def      a (     __a  )    ->      int:



					'''simple docstring'''






					if root is None:
										return 0

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

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

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

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

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

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

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

										UpperCamelCase__   ,							UpperCamelCase__  :Optional[Any]				   =					get_distrib(node.left  )
										UpperCamelCase__   ,							UpperCamelCase__  :Union[str, Any]				   =					get_distrib(node.right  )

										UpperCamelCase__  :Tuple				   =					1 - left_distrib_excess
										UpperCamelCase__  :Optional[int]				   =					1 - right_distrib_excess

										UpperCamelCase__  :int				   =					(
										    left_distrib_moves
										    + right_distrib_moves
										    + abs(__a  )
										    + abs(__a  )
										)
										UpperCamelCase__  :Optional[Any]				   =					node.data - coins_to_left - coins_to_right

										return CoinsDistribResult(__a					,   __a  )

					return get_distrib(__a  )[0]


if __name__ == "__main__":
		import doctest

		doctest.testmod()