"""simple docstring"""







def 						__UpperCAmelCase       (					UpperCAmelCase_					:       int    ,							UpperCAmelCase_					:       list						)							->    Dict:

	'''simple docstring'''





	_enforce_args(UpperCAmelCase_    ,							UpperCAmelCase_						)
	if n == 0:
		return 0
	__snake_case    :							List[str]   	=				float('-inf'						)
	for i in range(1    ,							n + 1						):
		__snake_case    :							List[str]   	=				max(
		    UpperCAmelCase_    ,							prices[i - 1] + naive_cut_rod_recursive(n - i    ,							UpperCAmelCase_						)						)

	return max_revue
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       int    ,							UpperCAmelCase_					:       list						)							->    Optional[Any]:

	'''simple docstring'''





	_enforce_args(UpperCAmelCase_    ,							UpperCAmelCase_						)
	__snake_case    :							List[str]   	=				[float('-inf'						) for _ in range(n + 1						)]
	return _top_down_cut_rod_recursive(UpperCAmelCase_    ,							UpperCAmelCase_    ,							UpperCAmelCase_						)
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       int    ,							UpperCAmelCase_					:       list    ,							UpperCAmelCase_					:       list						)							->    Optional[int]:

	'''simple docstring'''





	if max_rev[n] >= 0:
		return max_rev[n]
	elif n == 0:
		return 0
	else:
		__snake_case    :							str   	=				float('-inf'						)
		for i in range(1    ,							n + 1						):
			__snake_case    :							str   	=				max(
			    UpperCAmelCase_    ,							prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,							UpperCAmelCase_    ,							UpperCAmelCase_						)    ,							)

		__snake_case    :							List[str]   	=				max_revenue

	return max_rev[n]
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       int    ,							UpperCAmelCase_					:       list						)							->    Optional[int]:

	'''simple docstring'''





	_enforce_args(UpperCAmelCase_    ,							UpperCAmelCase_						)

	# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
	# length 0.
	__snake_case    :							str   	=				[float('-inf'						) for _ in range(n + 1						)]
	__snake_case    :							Optional[int]   	=				0

	for i in range(1    ,							n + 1						):
		__snake_case    :							Optional[Any]   	=				max_rev[i]
		for j in range(1    ,							i + 1						):
			__snake_case    :							List[str]   	=				max(UpperCAmelCase_    ,							prices[j - 1] + max_rev[i - j]						)

		__snake_case    :							str   	=				max_revenue_i

	return max_rev[n]
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       int    ,							UpperCAmelCase_					:       list						)							->    Optional[int]:

	'''simple docstring'''





	if n < 0:
		__snake_case    :							List[Any]   	=				F"n must be greater than or equal to 0. Got n = {n}"
		raise ValueError(UpperCAmelCase_						)

	if n > len(UpperCAmelCase_						):
		__snake_case    :							str   	=				(
		    'Each integral piece of rod must have a corresponding price. '
		    F"Got n = {n} but length of prices = {len(UpperCAmelCase_						)}"
		)
		raise ValueError(UpperCAmelCase_						)
def 						__UpperCAmelCase       (					)							->    Union[str, Any]:

	'''simple docstring'''





	__snake_case    :							Tuple   	=				[6, 10, 12, 15, 20, 23]
	__snake_case    :							List[str]   	=				len(UpperCAmelCase_						)

	# the best revenue comes from cutting the rod into 6 pieces, each
	# of length 1 resulting in a revenue of 6 * 6 = 36.
	__snake_case    :							Any   	=				36

	__snake_case    :							List[str]   	=				top_down_cut_rod(UpperCAmelCase_    ,							UpperCAmelCase_						)
	__snake_case    :							Optional[int]   	=				bottom_up_cut_rod(UpperCAmelCase_    ,							UpperCAmelCase_						)
	__snake_case    :							List[Any]   	=				naive_cut_rod_recursive(UpperCAmelCase_    ,							UpperCAmelCase_						)

	assert expected_max_revenue == max_rev_top_down
	assert max_rev_top_down == max_rev_bottom_up
	assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
	main()






"""simple docstring"""







def 						__UpperCAmelCase       (					UpperCAmelCase_					:       list[int]    ,							UpperCAmelCase_					:       str						)							->    list[int]:

	'''simple docstring'''





	__snake_case    :							Union[str, Any]   	=				int(UpperCAmelCase_						)

	# Initialize Result
	__snake_case    :							int   	=				[]

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

	return answer


# Driver Code
if __name__ == "__main__":
	_a  :  Optional[int]=				[]
	_a  :  Optional[int]=				"0"

	if (
	    input("Do you want to enter your denominations ? (yY/n): ").strip().lower()
	    == "y"
	):
		_a  :  int=				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()))
		_a  :  Optional[int]=				input("Enter the change you want to make in Indian Currency: ").strip()
	else:
		# All denominations of Indian Currency if user does not enter
		_a  :  Tuple=				[1, 2, 5, 10, 20, 50, 100, 500, 2_000]
		_a  :  List[str]=				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}: ''')
		_a  :  List[Any]=				find_minimum_change(denominations, value)
		# Print result
		for i in range(len(answer)):
			print(answer[i], end=" ")





