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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

# -*- coding:utf-8 -*-
import numpy as np

x = int(input())
num = [i for i in range(2, 100010)]
#print(num)

np_x = np.array(num)

for i in range(2, 100010):
    b = np.logical_or(np_x == i, np_x%i != 0)
    np_x = np_x[b]
#print(np_x)

ans = np_x[np_x >= x]
#print(ans)
print(ans[0])