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 (2.7.1) (judge verdict: Accepted)

require "set"
x = gets.chomp.to_i

MAX = 10 ** 5 + 1000
set = Set.new
2.upto(Math.sqrt(MAX)) do |i|
  next if set.include?(i)
  tmp = i * 2
  while tmp <= MAX do
    set << tmp
    tmp += i
  end
end

x.upto(MAX) do |i|
  unless set.include?(i)
    puts i
    exit
  end
end