





from __future__ import annotations

import math


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase				)    ->  float:
    lowerCamelCase__					:   Tuple      				=	u
    for i in range(1		,			_UpperCAmelCase				):
        lowerCamelCase__					:   Dict      				=	temp * (u - i)
    return temp


def  SCREAMING_SNAKE_CASE   ( )    ->  None:
    lowerCamelCase__					:   Optional[Any]      				=	int(input('enter the numbers of values: '				)				)
    lowerCamelCase__					:   list[list[float]]      				=	[]
    for _ in range(_UpperCAmelCase				):
        y.append([]				)
    for i in range(_UpperCAmelCase				):
        for j in range(_UpperCAmelCase				):
            y[i].append(_UpperCAmelCase				)
            lowerCamelCase__					:   Optional[int]      				=	0

    print('enter the values of parameters in a list: '				)
    lowerCamelCase__					:   List[Any]      				=	list(map(_UpperCAmelCase		,			input().split()				)				)

    print('enter the values of corresponding parameters: '				)
    for i in range(_UpperCAmelCase				):
        lowerCamelCase__					:   str      				=	float(input()				)

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

    # for calculating forward difference table

    for i in range(1		,			_UpperCAmelCase				):
        for j in range(n - i				):
            lowerCamelCase__					:   Union[str, Any]      				=	y[j + 1][i - 1] - y[j][i - 1]

    lowerCamelCase__					:   Optional[int]      				=	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()












from __future__ import annotations

from collections.abc import Generator


def  SCREAMING_SNAKE_CASE   ( )    ->  Generator[int, None, None]:
    lowerCamelCase__					:   dict[int, int]      				=	{}
    lowerCamelCase__					:   Union[str, Any]      				=	2
    while True:
        lowerCamelCase__					:   Optional[int]      				=	factor_map.pop(_UpperCAmelCase		,			_UpperCAmelCase				)
        if factor:
            lowerCamelCase__					:   Optional[Any]      				=	factor + prime
            while x in factor_map:
                x += factor
            lowerCamelCase__					:   Optional[Any]      				=	factor
        else:
            lowerCamelCase__					:   Union[str, Any]      				=	prime
            yield prime
        prime += 1


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 1e10				)    ->  int:
    lowerCamelCase__					:   Tuple      				=	sieve()

    lowerCamelCase__					:   Dict      				=	1
    while True:
        lowerCamelCase__					:   List[Any]      				=	next(_UpperCAmelCase				)
        if (2 * prime * n) > limit:
            return n
        # Ignore the next prime as the reminder will be 2.
        next(_UpperCAmelCase				)
        n += 2


if __name__ == "__main__":
    print(solution())





