



from math import factorial





def 					__snake_case     (      _UpperCAmelCase = 20    ):
    __a							=    2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
    # 2, 3,...
    __a							=    n // 2

    return int(factorial(_UpperCAmelCase    ) / (factorial(_UpperCAmelCase    ) * factorial(n - k    ))    )


if __name__ == "__main__":
 import sys

 if len(sys.argv) == 1:
  print(solution(20))
 else:
  try:
   __snake_case						:int						=					int(sys.argv[1])
   print(solution(n))
  except ValueError:
   print('''Invalid entry - please enter a number.''')










from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass

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


__snake_case						:Optional[Any]						=					namedtuple('''CoinsDistribResult''', '''moves excess''')





def 					__snake_case     (      _UpperCAmelCase    ):

    if root is None:
        return 0

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

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

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

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

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

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

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

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

        __a							=    1 - left_distrib_excess
        __a							=    1 - right_distrib_excess

        __a							=    (
            left_distrib_moves
            + right_distrib_moves
            + abs(_UpperCAmelCase    )
            + abs(_UpperCAmelCase    )
        )
        __a							=    node.data - coins_to_left - coins_to_right

        return CoinsDistribResult(_UpperCAmelCase       ,			_UpperCAmelCase    )

    return get_distrib(_UpperCAmelCase    )[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()





