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 Lua (5.3.2) (judge verdict: Accepted)

local x = io.read("*n")
while true do
  local lim = math.ceil(math.sqrt(x))
  local f = true
  for i = 2, lim do
    if x ~= i and x % i == 0 then
      f = false
      break
    end
  end
  if f then print(x) break else x = x + 1 end
end