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: Wrong Answer)

#include <iostream>
#include <bitset>

using namespace std;

int main() {
  int64_t X;
  cin >> X;
  bitset<10000001> b;
  b.set(2);
  for (int64_t i = 3; i <= 10000000; i += 2) {
    for (int64_t j = i + i; j <= 10000000; j += i) {
      b.set(j);
    }
  }
  int result = X | 1;
  if (result < 2) result = 2;
  while (b[result]) result += 2;
  cout << result << endl;
  return 0;
}