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 Pascal (FPC 3.0.4) (judge verdict: Accepted)

program hi;
var 
    si: array[2..100010] of boolean;
    x, i, j: longint;

begin
    for i := 2 to 100010 do 
        si[i] := true;
    for i := 2 to 317 do begin
        j := i * i;
        while j <= 100010 do begin
            si[j] := false;
            j := j + i;
        end;
    end;
    readln(x);
    if si[x] then 
        writeln(x)
    else begin
        i := x;
        while not si[i] do 
            inc(i);
        writeln(i);
    end;
end.