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 prime (n)
  return true if n == 2
  lim = Math.sqrt(n).ceil
  (2..lim).each do |i|
    return false if n % i == 0
  end
  true
end

if x == 2
  puts x
  exit 0
end

x += 1 if x % 2 == 0
while true do
  break if prime (x)
  x +=2
end

puts x