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: Time Limit Exceeded)

x = gets.chomp.to_i
list = (2..100000).to_a
prime_list = []
sqrt = Math.sqrt(x).floor
while true
    value = list[0]
    prime_list.push(value)
    list.delete_if{|num| num % value == 0}
    if list.size == 0
        break
    end
end
prime_list.push(100003)
first = prime_list.index {|v| v > x }
print prime_list[first]