Problem:
Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

2 \le X \le 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php

fscanf(STDIN, "%d", $x);

while (1) {
    if (isPrime($x)) {
        echo $x;
        return;
    }

    ++$x;
}

function isPrime($x) {
    if ($x <= 2) {
        return true;
    }

    if ($x % 2 === 0) {
        return false;
    }

    for ($i = 3; $i <= sqrt($x); $i += 2) {
        if ($x % $i === 0) {
            return false;
        }
    }

    return true;
}