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>
#define rep(i,n) for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef long double ld;
const double pi=acos(-1.0);
const ll mod=pow(10,9)+7;
const ll INF=pow(2,31)-1;
using str=string;
typedef pair<int,int> P;
typedef vector<int> vi;

ll gcd(ll x,ll y){
    ll r;
    while((r=x%y) !=0){
        x=y;
        y=r;
    }
    return y;
}

ll lcm(ll x, ll y){
    x /= gcd(x,y);
    y /=gcd(x,y);
    return (x*y);
}

bool prime(int n){
    if(n<=1) return false;
    for(int i=2;i*i<n;i++){
        if(n%i==0) return false;
    }
    return true;
}

int main(){
    int x,y;
    cin >> x;
    y=x;
    while(!prime(y)){
        y+=1;
    }
    cout << y << endl;
    return 0;
}