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;
#define reset(X) memset(X, 0, sizeof(X))
#define int long long
typedef long long ll;
#define pb push_back
#define se second
#define fi first
#define endl '\n'
#define all(X) X.begin(),X.end()

const int INF=1e18;
const int mod=1e9+7;
const int mod2=998244353;



#define REDN(a) int a;cin>>a;
#define REDL(a,n) int a[n];for(int i=0;i<n;i++) cin>>a[i];
#define REDA(a,n,m) int a[n][m];for(int i=0;i<n;i++)for(int j=0;j<m;j++) cin>>a[i][j];





int pow(int a, int b)
{
    int prod=1;
    int mult=a;
    while(b!=0)
    {
        if(b%2)
        {
            prod*=mult;
            prod%=mod2;
        }
        mult*=mult;
        mult%=mod2;
        b/=2;
    }
    return prod;
}
int mod_inv(int q, int mod)
{
    return pow(q, mod-2);
}




bool isPrime(int n)
{
    int k=sqrt(n);
    for(int i=2;i<=k;i++)
        if(n%i==0)
            return false;
    return true;
}

const int MAXN=4e5+10;
signed main()
{
    
    
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    #ifndef ONLINE_JUDGE
    if (fopen("INPUT.txt", "r")) {
        freopen ("INPUT.txt" , "r" , stdin);
        // freopen ("OUTPUT.txt" , "w" , stdout);
    }
    #endif
//---------------------------------------------------------------------------------------------------
    int x;
    cin>>x;
    while(!isPrime(x))
        x++;
    cout<<x;
}