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 (2.3.3) (judge verdict: Accepted)

x = gets.to_i

def check_prime(num)
  case num
  when 1 then
    false
  when 2 then
    true
  else
    (2..(num-1)).each do |index|
      if num % index == 0
        return false
      end
    end
    return true
  end
end

loop do
  if check_prime(x)
    puts x
    exit
  else
    x += 1
  end
end