
from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass

@dataclass
class __snake_case		:
    _a		:						int
    _a		:						TreeNode | None=    None
    _a		:						TreeNode | None=    None






lowercase  : int						   =							namedtuple("""CoinsDistribResult""", """moves excess""")







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   int:

       if root is None:
              return 0

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

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

       def count_coins(SCREAMING_SNAKE_CASE__    ) -> 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__    ) -> CoinsDistribResult:

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

              lowercase     ,      lowercase							:					Optional[int]	     =				get_distrib(node.left    )
              lowercase     ,      lowercase							:					Dict	     =				get_distrib(node.right    )

              lowercase							:					List[str]	     =				1 - left_distrib_excess
              lowercase							:					str	     =				1 - right_distrib_excess

              lowercase							:					Union[str, Any]	     =				(
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(SCREAMING_SNAKE_CASE__    )
                  + abs(SCREAMING_SNAKE_CASE__    )
              )
              lowercase							:					Dict	     =				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()


def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   int:

       def count_of_possible_combinations(SCREAMING_SNAKE_CASE__    ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              return sum(count_of_possible_combinations(target - item    ) for item in array    )

       return count_of_possible_combinations(SCREAMING_SNAKE_CASE__    )







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   int:

       def count_of_possible_combinations_with_dp_array(
           SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              if dp_array[target] != -1:
                     return dp_array[target]
              lowercase							:					Any	     =				sum(
                  count_of_possible_combinations_with_dp_array(target - item ,     SCREAMING_SNAKE_CASE__    )
                  for item in array    )
              lowercase							:					Optional[int]	     =				answer
              return answer

       lowercase							:					int	     =				[-1] * (target + 1)
       return count_of_possible_combinations_with_dp_array(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   int:
       lowercase							:					str	     =				[0] * (target + 1)
       lowercase							:					Tuple	     =				1

       for i in range(1 ,     target + 1    ):
              for j in range(SCREAMING_SNAKE_CASE__    ):
                     if i - array[j] >= 0:
                            dp_array[i] += dp_array[i - array[j]]

       return dp_array[target]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  lowercase  : Any						   =							3
  lowercase  : Optional[Any]						   =							5
  lowercase  : Tuple						   =							[1, 2, 5]
  print(combination_sum_iv(n, array, target))
