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)

n = int(input())
"""素因数分解"""
def factrize(n):
    b = 2
    fct = []
    while b*b <= n:
        while n % b == 0:
            n //= b
            #もし素因数を重複させたくないならここを加えてfct.append(b)を消す
            """
            if not b in fct:
                fct.append(b)
            """
            fct.append(b)
        b = b+1
    if n > 1:
        fct.append(n)
    return len(fct) == 1 #TFが帰る


while True:
    if factrize(n):
        break
    else:
        n+=1
print(n)