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)

#define _USE_MATH_DEFINES
#include <cstdio>
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <complex>
#include <string>
#include <vector>
#include <array>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <limits>
#include <climits>
#include <cfloat>
#include <functional>
#include <iterator>
using namespace std;

void findPrime(int N, vector<bool>& isPrime)
{
    isPrime.assign(N+1, true);
    isPrime[0] = isPrime[1] = false;
    for(int i=2; i*i<=N; i++){
        if(isPrime[i]){
            for(int j=i; i*j<=N; j++){
                isPrime[i*j] = false;
            }
        }
    }
}

int main()
{
    vector<bool> isPrime;
    findPrime(200000, isPrime);

    int x;
    cin >> x;
    while(!isPrime[x])
        ++ x;
    cout << x << endl;

    return 0;
}