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: Runtime Error)

import numpy as np
X =int(input())
 
if X == 2:
    print(X)
 
else:
    s = np.array([2])
    
    for i in range(2, 10**5 + 3):
        res = True
        for j in s:
            if (i % j) == 0:
                res = False
                break
        
        if res == True:
            s = np.append(s, i)
            if i >= X:
                print(i)
                break