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)

include Math
# 入力
X = gets.to_i

# 素数判定関数
def is_prime(n)
  if n == 2
    return true
  end
  cnt = 0
  2.upto Math.sqrt(n).ceil do |i|
    if n % i == 0
      return false
    end
  end
  return n != 1
end

X.upto 10e5 do |i|
  if is_prime(i)
    puts i
    exit
  end
end