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)

n = STDIN.gets.chomp.to_i

prime = []
# ルート 100000まででOK
max =  Math.sqrt(100000).round
[*(2..100003)].each do |x|
  p_flg = true
  prime.each do |y|
    if x % y == 0
      p_flg = false
    end
    if y >= max
      break
    end
  end
  if p_flg
    if x >= n
      puts x
      break
    end
    prime.push(x)
  end
end