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 Go (1.14.1) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var x int
	fmt.Scan(&x)

	ps := primes(110000)
	for !ps[x] {
		x++
	}
	fmt.Println(x)
}

func primes(n int) []bool {
	ps := make([]bool, n+1)
	for i := 2; i <= n; i++ {
		ps[i] = true
	}
	for i := 2; i <= n; i++ {
		if ps[i] {
			for j := i + i; j <= n; j += i {
				ps[j] = false
			}
		}
	}
	return ps
}