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: Runtime Error)

import argparse
import itertools

def make_parser():
    parser = argparse.ArgumentParser()

    parser.add_argument('X', type=int)
    args = parser.parse_args()

    return args

def main():
    args = make_parser()
    number = args.X
    flag = 0

    if(number%2 == 0):
        number += 1
    else:
        pass

    while(True):
        for i in range(2, number):
            if number%i == 0:
                number += 2
                break

            elif i == (number-1):
                flag = 1
                print(number)
                break

            else:
                pass

        if flag == 1:
            break


if __name__ == "__main__":
    main()