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 2.6.2) (judge verdict: Wrong Answer)

uses crt;
var
        so,k,i:longint;
function check(so:longint):boolean;
begin
   if (so = 2 ) or (so = 3) then exit(true);
   if (so = 1) or (so = 0) or (so mod 2 = 0) or (so mod 3 = 0) then exit(false);
   k:=-1;
   repeat
       inc(k,6);
       if (so mod k = 0) or (so mod k+2=0) then break;
   until (k>trunc(sqrt(so)));
   exit(k>trunc(sqrt(so)));
end;
begin
    clrscr;
    readln(so);
    for i:=so to so*10 do
    begin
        if check(i) then
        begin
            write(i);
            break;
        end;
    end;
    readln;
end.