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 (7.3.0) (judge verdict: Accepted)

n = int(input())
primes = []
def is_prime(k):
    if k < 2:
        return False
    if k == 2:
        return True
    for p in primes:
        if k % p == 0:
            return False
        if k <= p*p:
            break
    return True


for i in range(1000000 + 100):
    if is_prime(i):
        primes.append(i)
        if i >= n:
            print(i)
            break