'''simple docstring'''


__lowerCAmelCase	:       Dict						       =	0  # The first color of the flag.
__lowerCAmelCase	:       Optional[Any]						       =	1  # The second color of the flag.
__lowerCAmelCase	:       List[Any]						       =	2  # The third color of the flag.
__lowerCAmelCase	:       int						       =	(red, white, blue)





def       lowerCAmelCase					(		UpperCamelCase__				:   list       ):


	"""simple docstring"""
	if not sequence:
		return []
	if len(UpperCamelCase__       ) == 1:
		return list(UpperCamelCase__       )
	__UpperCAmelCase							=			0
	__UpperCAmelCase							=			len(UpperCamelCase__       ) - 1
	__UpperCAmelCase							=			0
	while mid <= high:
		if sequence[mid] == colors[0]:
			__UpperCAmelCase				,			__UpperCAmelCase							=			sequence[mid], sequence[low]
			low += 1
			mid += 1
		elif sequence[mid] == colors[1]:
			mid += 1
		elif sequence[mid] == colors[2]:
			__UpperCAmelCase				,			__UpperCAmelCase							=			sequence[high], sequence[mid]
			high -= 1
		else:
			__UpperCAmelCase							=			f"""The elements inside the sequence must contains only {colors} values"""
			raise ValueError(UpperCamelCase__       )
	return sequence


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					__lowerCAmelCase	:       List[str]						       =	input("Enter numbers separated by commas:\n").strip()
					__lowerCAmelCase	:       int						       =	[int(item.strip()) for item in user_input.split(",")]
					print(F"""{dutch_national_flag_sort(unsorted)}""")

'''simple docstring'''


from __future__ import annotations

import math





def       lowerCAmelCase					(		UpperCamelCase__				:   float    ,					UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			u
	for i in range(1    ,					UpperCamelCase__       ):
		__UpperCAmelCase							=			temp * (u - i)
	return temp





def       lowerCAmelCase					(		):


	"""simple docstring"""
	__UpperCAmelCase							=			int(input('''enter the numbers of values: '''       )       )
	__UpperCAmelCase							=			[]
	for _ in range(UpperCamelCase__       ):
		y.append([]       )
	for i in range(UpperCamelCase__       ):
		for j in range(UpperCamelCase__       ):
			y[i].append(UpperCamelCase__       )
			__UpperCAmelCase							=			0

	print('''enter the values of parameters in a list: '''       )
	__UpperCAmelCase							=			list(map(UpperCamelCase__    ,					input().split()       )       )

	print('''enter the values of corresponding parameters: '''       )
	for i in range(UpperCamelCase__       ):
		__UpperCAmelCase							=			float(input()       )

	__UpperCAmelCase							=			int(input('''enter the value to interpolate: '''       )       )
	__UpperCAmelCase							=			(value - x[0]) / (x[1] - x[0])

	# for calculating forward difference table

	for i in range(1    ,					UpperCamelCase__       ):
		for j in range(n - i       ):
			__UpperCAmelCase							=			y[j + 1][i - 1] - y[j][i - 1]

	__UpperCAmelCase							=			y[0][0]
	for i in range(1    ,					UpperCamelCase__       ):
		summ += (ucal(UpperCamelCase__    ,					UpperCamelCase__       ) * y[0][i]) / math.factorial(UpperCamelCase__       )

	print(f"""the value at {value} is {summ}"""       )


if __name__ == "__main__":
					main()
