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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

/**
 * @param input number
 */
function Main(input) {
  // 偶数のみで検証するため2は含まない
  const prevPrimes = [];

  if (num === 2) {
    console.log(2);
    return;
  }

  var num;
  const sqrt = Math.sqrt(input);
  for (num = 3; num <= sqrt; num += 2) {
    if (isPrime(num, prevPrimes)) {
      prevPrimes.push(num);
    }
  }
  for (num = input + 1 - input % 2; true; num += 2) {
    if (isPrime(num, prevPrimes)) {
      break;
    }
  }

  console.log(prevPrimes);

  console.log(num);
}

function isPrime(num, prevPrimes) {
  return prevPrimes.every((prime) => num % prime);
}

Main(+require("fs").readFileSync("/dev/stdin", "utf8").trim());