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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

my $x = glob <>;
my @prime;

$i = 1;
while (1) {
    $i++;

    my $is_prime = 1;
    for ( my $j = 2 ; $j < $i // 2 ; $j++ ) {
        if ( $i % $j == 0 ) {
            $is_prime = 0;
            last;
        }
    }

    if ( not $is_prime ) {
        next;
    }

    if ( $i >= $x ) {
        last;
    }
    push( @prime, $i );
}

print($i)