"""simple docstring"""






from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass





@dataclass
class  _A						:
      snake_case__			:   int
      snake_case__			:   TreeNode | None							  =	None
      snake_case__			:   TreeNode | None							  =	None






__lowerCAmelCase    :       str					     =namedtuple("""CoinsDistribResult""", """moves excess""")


def 			UpperCAmelCase__       (				lowerCAmelCase__     :TreeNode | None		) ->    int:
      '''simple docstring'''


      if root is None:
            return 0

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

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

      def count_coins(lowerCAmelCase__     :TreeNode | None		) -> 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__     :TreeNode | None		) -> 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(lowerCAmelCase__		)
                + abs(lowerCAmelCase__		)
            )
            lowercase														=	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 decimal import Decimal, getcontext
from math import ceil, factorial


def 			UpperCAmelCase__       (				lowerCAmelCase__     :int		) ->    str:
      '''simple docstring'''


      if not isinstance(lowerCAmelCase__					,		lowerCAmelCase__		):
            raise TypeError("""Undefined for non-integers"""		)
      elif precision < 1:
            raise ValueError("""Undefined for non-natural numbers"""		)

      lowercase														=	precision
      lowercase														=	ceil(precision / 1_4		)
      lowercase														=	4_2_6_8_8_0 * Decimal(1_0_0_0_5		).sqrt()
      lowercase														=	1
      lowercase														=	1_3_5_9_1_4_0_9
      lowercase														=	Decimal(lowerCAmelCase__		)
      for k in range(1					,		lowerCAmelCase__		):
            lowercase														=	factorial(6 * k		) // (factorial(3 * k		) * factorial(lowerCAmelCase__		) ** 3)
            linear_term += 5_4_5_1_4_0_1_3_4
            exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
            partial_sum += Decimal(multinomial_term * linear_term		) / exponential_term
      return str(constant_term / partial_sum		)[:-1]


if __name__ == "__main__":
       __lowerCAmelCase    :       List[Any]					     =5_0
       print(F"""The first {n} digits of pi is: {pi(n)}""")



