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 main;
const
  max = 100010;

var
  n, ans, i, j : longint;
  prime : array [1..max] of boolean;

begin
  readln(n);
  for i := 2 to max do
    prime[i] := true;
  for i := 2 to trunc(sqrt(max)) do
    if prime[i] then
      for j := 2 to (max div i) do
        prime[i*j] := false;
  for i := 1 to max do
    if (i >= n) and prime[i] then begin
      ans := i;
      break;
    end;
  writeln(ans);
end.