
from __future__ import annotations

import math
from collections.abc import Callable


def 						UpperCAmelCase			(	a_		,   a_		,   a_		,   a_ = 1_0_0		,   )		->	float:







				"""simple docstring"""



				__A   			= x_start
				__A   			= fnc(a_						)
				__A   			= 0.0

				for _ in range(a_						):
								# Approximates curve as a sequence of linear lines and sums their length
								__A   			= (x_end - x_start) / steps + xa
								__A   			= fnc(a_						)
								length += math.hypot(xa - xa		,   fxa - fxa						)

								# Increment step
								__A   			= xa
								__A   			= fxa

				return length


if __name__ == "__main__":


					def 						UpperCAmelCase			(	a_						)		->	Optional[int]:







									"""simple docstring"""



									return math.sin(1_0 * x						)

					print('f(x) = sin(10 * x)')
					print('The length of the curve from x = -10 to x = 10 is:')
					SCREAMING_SNAKE_CASE							:Tuple							 =				10
					while i <= 10_0000:
										print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
										i *= 10



'''simple docstring'''



def    a__       (  a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      int(a__						)

     # Initialize Result
     __SCREAMING_SNAKE_CASE     =      []

     # 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__":
  UpperCAmelCase :       Dict			   =     []
  UpperCAmelCase :       List[str]			   =     '0'

  if (
      input('Do you want to enter your denominations ? (yY/n): ').strip().lower()
      == "y"
  ):
    UpperCAmelCase :       List[str]			   =     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()))
    UpperCAmelCase :       str			   =     input('Enter the change you want to make in Indian Currency: ').strip()
  else:
    # All denominations of Indian Currency if user does not enter
    UpperCAmelCase :       int			   =     [1, 2, 5, 1_0, 2_0, 5_0, 1_0_0, 5_0_0, 2_0_0_0]
    UpperCAmelCase :       Any			   =     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}: """)
    UpperCAmelCase :       Any			   =     find_minimum_change(denominations, value)
    # Print result
    for i in range(len(answer)):
      print(answer[i], end=' ')






