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: Accepted)


var n,i,j,max: longint;
snt: array[1..1000000] of boolean;
begin

read(n);
max:=n*10;
for j:=1 to max do snt[j]:=true;
snt[1]:=false;
j:=2;
while j<=trunc(sqrt(max)) do
begin
while snt[j]=false do inc(j);
for i:=2 to max div j do snt[i*j]:=false;
inc(j);
end;
while snt[n]=false do inc(n);
write(n);

end.