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)

total = 9593
primes = [0] * total
primes[0] = 2
x = 1
k = 1
while (k < total):
    x += 2
    j = 0;
    while (j < k and x % primes[j] != 0):
        if (primes[j] * primes[j] >= x):
            primes[k] = x
            k = k + 1
            break
        j = j + 1
# print(primes)

X = int(input())
for p in primes:
    if p >= X:
        print(p)
        exit()