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 LuaJIT (2.0.4) (judge verdict: Accepted)

X=io.read"*n"

function f(x)
	if(x==2)then return true end
	if(x%2==0)then return false end
	for i=3,math.sqrt(x),2 do
		if(x%i==0)then return false end
	end
	return true
end

while(true)do
	if(f(X))then print(X)return end
	X=X+1
end