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 Ruby (2.7.1) (judge verdict: Accepted)

x = gets.to_i
is_prime = [true] * 200000

(2...200000).each{|a|
    if is_prime[a]
        ((a * 2)...200000).step(a){|m|
            is_prime[m] = false
        }
    end
}

(x...200000).each{|n|
    if is_prime[n]
        puts n
        break
    end
}