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<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<map>
#include<queue>
#include<string>
#include<iostream>

#define maxn 200005
#define INF 0x3f3f3f3f

using namespace std;

inline long long getint()
{
    long long num=0,flag=1;char c;
    while((c=getchar())<'0'||c>'9')if(c=='-')flag=-1;
    while(c>='0'&&c<='9')num=num*10+c-48,c=getchar();
    return num*flag;
}

int num;
int pri[maxn],np[maxn],cnt;

int main()
{
	num=getint();
	for(int i=2;i<maxn;i++)
	{
		if(!np[i])
		{
			pri[++cnt]=i;
			if(i>=num){printf("%d\n",i);return 0;}
		}
		for(int j=1;j<=cnt&&i*pri[j]<maxn;j++)
		{
			np[i*pri[j]]=1;
			if(i%pri[j]==0)break;
		}
	}
}