


"""simple docstring"""







def 					a__			(				SCREAMING_SNAKE_CASE    :    int				,      SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  while b:
    lowerCAmelCase						,  lowerCAmelCase     :     Any								=							b, a % b
  return a
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				,      SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  return a if b == 0 else euclidean_gcd_recursive(SCREAMING_SNAKE_CASE				,      a % b				)
def 					a__			(				):


  '''simple docstring'''







  print(f"""euclidean_gcd(3, 5) = {euclidean_gcd(3				,      5				)}"""				)
  print(f"""euclidean_gcd(5, 3) = {euclidean_gcd(5				,      3				)}"""				)
  print(f"""euclidean_gcd(1, 3) = {euclidean_gcd(1				,      3				)}"""				)
  print(f"""euclidean_gcd(3, 6) = {euclidean_gcd(3				,      6				)}"""				)
  print(f"""euclidean_gcd(6, 3) = {euclidean_gcd(6				,      3				)}"""				)

  print(f"""euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3				,      5				)}"""				)
  print(f"""euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5				,      3				)}"""				)
  print(f"""euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1				,      3				)}"""				)
  print(f"""euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3				,      6				)}"""				)
  print(f"""euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6				,      3				)}"""				)


if __name__ == "__main__":
     main()









"""simple docstring"""







from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass


@dataclass
class       SCREAMING_SNAKE_CASE__				:
       """simple docstring"""


       a  :				int
       a  :				TreeNode | None   =None
       a  :				TreeNode | None   =None

lowerCAmelCase__      				=   namedtuple('''CoinsDistribResult''', '''moves excess''')
def 					a__			(				SCREAMING_SNAKE_CASE    :    TreeNode | None				):


  '''simple docstring'''







  if root is None:
    return 0

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

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

  def count_coins(SCREAMING_SNAKE_CASE    :    TreeNode | None				) -> 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    :    TreeNode | None				) -> CoinsDistribResult:

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

    lowerCAmelCase						,  lowerCAmelCase     :     List[str]								=							get_distrib(node.left				)
    lowerCAmelCase						,  lowerCAmelCase     :     List[str]								=							get_distrib(node.right				)

    lowerCAmelCase     :     Union[str, Any]								=							1 - left_distrib_excess
    lowerCAmelCase     :     List[Any]								=							1 - right_distrib_excess

    lowerCAmelCase     :     int								=							(
        left_distrib_moves
        + right_distrib_moves
        + abs(SCREAMING_SNAKE_CASE				)
        + abs(SCREAMING_SNAKE_CASE				)
    )
    lowerCAmelCase     :     int								=							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()





