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)

def prime?(n)
  return false if n < 2
  return true  if n == 2 or n == 3
  return false if (n % 2).zero? or (n % 3).zero?
  i, step = 5, 2
  guard = Math.sqrt(n).to_i
  while i <= guard
    return false if (n % i).zero?
    i += step
    step = 6 - step
  end
  true
end

def action(n)
  return n if prime?(n)
  if n.even?
    action(n+1)
  else
    action(n+2)
  end
end

x = gets.chop.to_i

print action(x)