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: Accepted)

import math
x = input()
x = int(x)
if x in [2,3,5,7]:
    print(x)
elif x == 4:
    print(5)
elif x==6:
    print(7)
elif x==8:
    print(11)
else:
    while 1:
        flag = 0
        if x%2==0:
            x= x+1
            continue
        y = 3
        while y<math.sqrt(x):
            if x%y==0:
                break
            y=y+2
            if y>math.sqrt(x):
                flag=1
                break
        if flag == 1:
            print(x)
            break
        x = x+2