


"""simple docstring"""







from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass




@dataclass
class 				UpperCamelCase_			:

	"""simple docstring"""





	snake_case__       :						int
	snake_case__       :						TreeNode | None					      =    None
	snake_case__       :						TreeNode | None					      =    None


a__       :							List[Any]        =  namedtuple('''CoinsDistribResult''', '''moves excess''')




def      UpperCAmelCase__ (lowerCAmelCase_     ):




					'''simple docstring'''


					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     )

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

										__SCREAMING_SNAKE_CASE		     =       1 - left_distrib_excess
										__SCREAMING_SNAKE_CASE		     =       1 - right_distrib_excess

										__SCREAMING_SNAKE_CASE		     =       (
										    left_distrib_moves
										    + right_distrib_moves
										    + abs(lowerCAmelCase_     )
										    + abs(lowerCAmelCase_     )
										)
										__SCREAMING_SNAKE_CASE		     =       node.data - coins_to_left - coins_to_right

										return CoinsDistribResult(lowerCAmelCase_						,		lowerCAmelCase_     )

					return get_distrib(lowerCAmelCase_     )[0]


if __name__ == "__main__":
		import doctest

		doctest.testmod()




"""simple docstring"""







from math import asin, atan, cos, radians, sin, sqrt, tan

a__       :							List[str]        =  6_37_81_37.0
a__       :							Tuple        =  6_35_67_52.31_42_45
a__       :							str        =  6_3_7_8_1_3_7




def      UpperCAmelCase__ (lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_     ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE		     =       (AXIS_A - AXIS_B) / AXIS_A
					__SCREAMING_SNAKE_CASE		     =       atan((1 - flattening) * tan(radians(lowerCAmelCase_     )     )     )
					__SCREAMING_SNAKE_CASE		     =       atan((1 - flattening) * tan(radians(lowerCAmelCase_     )     )     )
					__SCREAMING_SNAKE_CASE		     =       radians(lowerCAmelCase_     )
					__SCREAMING_SNAKE_CASE		     =       radians(lowerCAmelCase_     )
					# Equation
					__SCREAMING_SNAKE_CASE		     =       sin((phi_a - phi_a) / 2     )
					__SCREAMING_SNAKE_CASE		     =       sin((lambda_a - lambda_a) / 2     )
					# Square both values
					sin_sq_phi *= sin_sq_phi
					sin_sq_lambda *= sin_sq_lambda
					__SCREAMING_SNAKE_CASE		     =       sqrt(sin_sq_phi + (cos(lowerCAmelCase_     ) * cos(lowerCAmelCase_     ) * sin_sq_lambda)     )
					return 2 * RADIUS * asin(lowerCAmelCase_     )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
