




'''simple docstring'''


import operator
def 						lowerCamelCase__   (				a    ,	a = False    ,	a = None							):
						__snake_case						 =   operator.lt if reverse else operator.gt
						__snake_case						 =   solution or []

						if not arr:
												return solution

						__snake_case						 =   [arr.pop(0							)]
						for i, item in enumerate(a							):
												if _operator(a    ,	sublist[-1]							):
																		sublist.append(a							)
																		arr.pop(a							)

    #  merging sublist into solution list
						if not solution:
												solution.extend(a							)
						else:
												while sublist:
																		__snake_case						 =   sublist.pop(0							)
																		for i, xx in enumerate(a							):
																								if not _operator(a    ,	a							):
																														solution.insert(a    ,	a							)
																														break
																		else:
																								solution.append(a							)

						strand_sort(a    ,	a    ,	a							)
						return solution


if __name__ == "__main__":
	assert strand_sort([4, 3, 5, 1, 2]) == [1, 2, 3, 4, 5]
	assert strand_sort([4, 3, 5, 1, 2], reverse=True) == [5, 4, 3, 2, 1]







'''simple docstring'''


from __future__ import annotations

import math
def 						lowerCamelCase__   (				a    ,	a							):
						__snake_case						 =   u
						for i in range(1    ,	a							):
												__snake_case						 =   temp * (u - i)
						return temp
def 						lowerCamelCase__   (				):
						__snake_case						 =   int(input('enter the numbers of values: '							)							)
						__snake_case						 =   []
						for _ in range(a							):
												y.append([]							)
						for i in range(a							):
												for j in range(a							):
																		y[i].append(a							)
																		__snake_case						 =   0

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

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

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

						# for calculating forward difference table

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

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

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


if __name__ == "__main__":
	main()

