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)

input = gets.chomp.to_i
ans = 0
#2の倍数かどうかのフラグ
isBinary = false

while true do
  #素数の確認は半分で良い
  half = input / 2 + 1
  #素数かどうかのフラグ
  flag = true
  half.times do |i|
    next if i <= 1
    if input != i && input % i == 0
      #素数でない場合
      flag = false
      break
    end
  end
  
  if flag
    ans = input
    break
  end
  
  #isBinaryがtrueの場合は１つ飛ばしにする
  if isBinary
    input += 2
    next
  end

  if input % 2 == 0
    input += 1
    isBinary = true
    next
  end
    
  input += 1
end

puts ans