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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

bool m[1000010];
void sieve()
{
    m[0]=false;
    m[1]=false;
    for(int i=2;i<1000010;i++)
        {
            m[i]=true;
        }
    for(int i=2;i*i<1000010;i++)
    {
        if(m[i]==true)
        {
            for(int j=i*i;j<1000010;j+=i)
            {
                m[j]=false;
            }
        }
    }
}

int main()
{
    int n;
    cin>>n;
    sieve();
    for(int i=n;;i++)
    {
        if(m[i])
        {
            cout<<i<<endl;
            break;
        }
    }
}