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<iostream>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<stack>
#include<queue>
#include<vector>
using namespace std;
bool arr[100100];
vector<long long int>v;
void sieve()
{
    long long int a, b, c, i, j, k;
    v.push_back(2);
    for (i = 3; i * i <= 100050; i = i + 2)
    {
        if (arr[i] == false)
        {
            v.push_back(i);
            for (j = i * i; j <= 100050; j = j + i)
            {
                arr[j] = true;
            }
        }
    }
    for (; i <= 100050; i = i + 2)
    {
        if (arr[i] == false)
            v.push_back(i);
    }

}
int main()
{
	long long int a, b, c, d, i, j, k, m, l, t;
    sieve();
    cin >> a;
    l = 0;
    long long int h = v.size() - 1;
   auto it= lower_bound(v.begin(), v.end(), a);
   b = it - v.begin();
   cout << v[b] << endl;
  
    return 0;
}