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 (LuaJIT 2.1.0) (judge verdict: Accepted)

x = io.read("*n")

not_prime = {true}

for i = 2, 10 ^ 6 do
  if not_prime[i] == nil then
    if i >= x then
      print(i)
      break
    end
    cur = i * 2
    while cur < 10 ^ 6 do
      not_prime[cur] = true
      cur = cur + i
    end
  end
end