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 <map>

template<long long sieve_N>
struct primes
{
	bool sieve[sieve_N];
	constexpr primes() : sieve()
	{
		for (long long i = 2; i < sieve_N; ++i)
		{
			sieve[i] = true;
		}
		sieve[0] = sieve[1] = false;
		for (long long i = 2; i < sieve_N; ++i)
		{
			for (long long j = i * i; j < sieve_N; j += i)
			{
				sieve[j] = false;
			}
		}
	}
};

constexpr primes<150000> p;

int main()
{
  int x;
  scanf("%d", &x);
  while (!p.sieve[x]) ++x;
  printf("%d\n", x);
  return 0;
}