



from __future__ import annotations

import math






def 			lowerCAmelCase__	(					lowerCamelCase_	:	float ,lowerCamelCase_	:	int):





				'''simple docstring'''

				lowerCAmelCase__  :       Optional[int]				=  u
				for i in range(1 ,lowerCamelCase_):
								lowerCAmelCase__  :       Optional[Any]				=  temp * (u - i)
				return temp






def 			lowerCAmelCase__	(					):





				'''simple docstring'''

				lowerCAmelCase__  :       Optional[int]				=  int(input('''enter the numbers of values: '''))
				lowerCAmelCase__  :       list[list[float]]				=  []
				for _ in range(lowerCamelCase_):
								y.append([])
				for i in range(lowerCamelCase_):
								for j in range(lowerCamelCase_):
												y[i].append(lowerCamelCase_)
												lowerCAmelCase__  :       int				=  0

				print('''enter the values of parameters in a list: ''')
				lowerCAmelCase__  :       Optional[int]				=  list(map(lowerCamelCase_ ,input().split()))

				print('''enter the values of corresponding parameters: ''')
				for i in range(lowerCamelCase_):
								lowerCAmelCase__  :       List[str]				=  float(input())

				lowerCAmelCase__  :       Union[str, Any]				=  int(input('''enter the value to interpolate: '''))
				lowerCAmelCase__  :       Optional[int]				=  (value - x[0]) / (x[1] - x[0])

				# for calculating forward difference table

				for i in range(1 ,lowerCamelCase_):
								for j in range(n - i):
												lowerCAmelCase__  :       List[Any]				=  y[j + 1][i - 1] - y[j][i - 1]

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

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


if __name__ == "__main__":
							main()






def 			lowerCAmelCase__	(					lowerCamelCase_	:	Any ,lowerCamelCase_	:	Optional[Any]):





				'''simple docstring'''

				lowerCAmelCase__  :       str				=  [0 for i in range(r + 1)]
				# nc0 = 1
				lowerCAmelCase__  :       Tuple				=  1
				for i in range(1 ,n + 1):
								# to compute current row from previous row.
								lowerCAmelCase__  :       Optional[int]				=  min(lowerCamelCase_ ,lowerCamelCase_)
								while j > 0:
												c[j] += c[j - 1]
												j -= 1
				return c[r]

print(binomial_coefficient(n=1_0, r=5))

