



def        a__     (				lowerCAmelCase__				):
      UpperCAmelCase_      			=							int(SCREAMING_SNAKE_CASE__				)
      if n_element < 1:
            UpperCAmelCase_      			=							ValueError("a should be a positive number"				)
            raise my_error

      UpperCAmelCase_      			=							[1]
      UpperCAmelCase_			,   UpperCAmelCase_			,   UpperCAmelCase_      			=							(0, 0, 0)
      UpperCAmelCase_      			=							1
      while index < n_element:
            while hamming_list[i] * 2 <= hamming_list[-1]:
                  i += 1
            while hamming_list[j] * 3 <= hamming_list[-1]:
                  j += 1
            while hamming_list[k] * 5 <= hamming_list[-1]:
                  k += 1
            hamming_list.append(
                min(hamming_list[i] * 2     ,      hamming_list[j] * 3     ,      hamming_list[k] * 5				)				)
            index += 1
      return hamming_list


if __name__ == "__main__":
  lowerCamelCase       	=						input("""Enter the last number (nth term) of the Hamming Number Series: """)
  print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
  lowerCamelCase       	=						hamming(int(n))
  print("""-----------------------------------------------------""")
  print(F"The list with nth numbers is: {hamming_numbers}")
  print("""-----------------------------------------------------""")









"""simple docstring"""





from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 				lowercase__       :







       '''simple docstring'''


       UpperCamelCase						=					42
       UpperCamelCase						=					None
       UpperCamelCase						=					None



lowerCamelCase       	=						namedtuple("""CoinsDistribResult""", """moves excess""")
def        a__     (				lowerCAmelCase__				):

      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				)

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

            UpperCAmelCase_      			=							1 - left_distrib_excess
            UpperCAmelCase_      			=							1 - right_distrib_excess

            UpperCAmelCase_      			=							(
                left_distrib_moves
                + right_distrib_moves
                + abs(lowerCAmelCase__				)
                + abs(lowerCAmelCase__				)
            )
            UpperCAmelCase_      			=							node.data - coins_to_left - coins_to_right

            return CoinsDistribResult(lowerCAmelCase__     ,      lowerCAmelCase__				)

      return get_distrib(lowerCAmelCase__				)[0]


if __name__ == "__main__":
  import doctest

  doctest.testmod()




