




def lowerCamelCase__       (      _lowercase = 200				):

  '''simple docstring'''


  UpperCAmelCase_      :							Optional[int]       =      [1, 2, 5, 10, 20, 50, 100, 200]
  UpperCAmelCase_      :							Optional[int]       =      [0] * (pence + 1)
  UpperCAmelCase_      :							Optional[Any]       =      1  # base case: 1 way to make 0 pence

  for coin in coins:
    for i in range(snake_case__			,						pence + 1			,						1				):
      number_of_ways[i] += number_of_ways[i - coin]
  return number_of_ways[pence]


if __name__ == "__main__":
     assert solution(200) == 73_682





from __future__ import annotations

from fractions import Fraction







def lowerCamelCase__       (      _lowercase			,						_lowercase				):

     '''simple docstring'''


     return (
         num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
     )







def lowerCamelCase__       (      _lowercase				):

     '''simple docstring'''


     UpperCAmelCase_      :							Optional[int]       =      []
     UpperCAmelCase_      :							Tuple       =      11
     UpperCAmelCase_      :							int       =      int('''1''' + '''0''' * digit_len				)
     for num in range(_lowercase			,						_lowercase				):
          while den <= 99:
               if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                    if is_digit_cancelling(_lowercase			,						_lowercase				):
                         solutions.append(f'''{num}/{den}'''				)
               den += 1
          num += 1
          UpperCAmelCase_      :							Any       =      10
     return solutions







def lowerCamelCase__       (      _lowercase = 2				):

     '''simple docstring'''


     UpperCAmelCase_      :							Tuple       =      1.0
     for fraction in fraction_list(_lowercase				):
          UpperCAmelCase_      :							Optional[Any]       =      Fraction(_lowercase				)
          result *= frac.denominator / frac.numerator
     return int(_lowercase				)


if __name__ == "__main__":
     print(solution())