
'''simple docstring'''




from decimal import Decimal, getcontext
from math import ceil, factorial







def 		lowerCAmelCase_				(   snake_case__						):




    '''simple docstring'''



    if not isinstance(snake_case__		,				snake_case__						):
        raise TypeError('''Undefined for non-integers'''						)
    elif precision < 1:
        raise ValueError('''Undefined for non-natural numbers'''						)

    A       :   Optional[int]					=						precision
    A       :   str					=						ceil(precision / 14						)
    A       :   List[str]					=						42_6880 * Decimal(1_0005						).sqrt()
    A       :   List[str]					=						1
    A       :   Tuple					=						1359_1409
    A       :   List[Any]					=						Decimal(snake_case__						)
    for k in range(1		,				snake_case__						):
        A       :   List[Any]					=						factorial(6 * k						) // (factorial(3 * k						) * factorial(snake_case__						) ** 3)
        linear_term += 5_4514_0134
        exponential_term *= -26_2537_4126_4076_8000
        partial_sum += Decimal(multinomial_term * linear_term						) / exponential_term
    return str(constant_term / partial_sum						)[:-1]


if __name__ == "__main__":
      lowercase			:				int    		=			50
      print(f'''The first {n} digits of pi is: {pi(n)}''')









'''simple docstring'''





def lowerCAmelCase  (__A  ,	__A):



     """simple docstring"""



     _a      =  int(__A)

     # Initialize Result
     _a      =  []

     # Traverse through all denomination
     for denomination in reversed(__A):
          # Find denominations
          while int(__A) >= int(__A):
               total_value -= int(__A)
               answer.append(__A)  # Append the "answers" array

     return answer


# Driver Code
if __name__ == "__main__":
  lowercase_		       =  []
  lowercase_		       =  "0"

  if (
      input("Do you want to enter your denominations ? (yY/n): ").strip().lower()
      == "y"
  ):
    lowercase_		       =  int(input("Enter the number of denominations you want to add: ").strip())

    for i in range(0, n):
      denominations.append(int(input(F"""Denomination {i}: """).strip()))
    lowercase_		       =  input("Enter the change you want to make in Indian Currency: ").strip()
  else:
    # All denominations of Indian Currency if user does not enter
    lowercase_		       =  [1, 2, 5, 10, 20, 50, 100, 500, 2_000]
    lowercase_		       =  input("Enter the change you want to make: ").strip()

  if int(value) == 0 or int(value) < 0:
    print("The total value cannot be zero or negative.")

  else:
    print(F"""Following is minimal change for {value}: """)
    lowercase_		       =  find_minimum_change(denominations, value)
    # Print result
    for i in range(len(answer)):
      print(answer[i], end=" ")



