#### Newton Forward Interpolation

p
```# https://www.geeksforgeeks.org/newton-forward-backward-interpolation/
from __future__ import annotations

import math

# for calculating u value
def ucal(u: float, p: int) -> float:
"""
>>> ucal(1, 2)
0
>>> ucal(1.1, 2)
0.11000000000000011
>>> ucal(1.2, 2)
0.23999999999999994
"""
temp = u
for i in range(1, p):
temp = temp * (u - i)
return temp

def main() -> None:
n = int(input("enter the numbers of values: "))
y: list[list[float]] = []
for _ in range(n):
y.append([])
for i in range(n):
for j in range(n):
y[i].append(j)
y[i][j] = 0

print("enter the values of parameters in a list: ")
x = list(map(int, input().split()))

print("enter the values of corresponding parameters: ")
for i in range(n):
y[i][0] = float(input())

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

# for calculating forward difference table

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

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

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

if __name__ == "__main__":
main()
```