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 PyPy3 (2.4.0) (judge verdict: Accepted)

x = int(input())

def fanc(s, x):
    for i in range(x + x, len(s), x):
        s[i] = False

def furui(n):
    s = [True] * n
    for x in range(2, int(n**0.5) + 1):
        if s[x]:
        	fanc(s, x)
    return [i for i in range(0,n) if s[i] and i > 1]

list = furui(10**6)
for i in range(len(list)):
	if list[i] >= x:
		print(list[i])
		exit(0)