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)

A = int(input())
if A == 2:
    print(2)
    exit()
sosu = [2] #素数が入る
sosu_2 = [4] #素数の2乗の数が入る
sosu_2_index = 1
for num in range(3, 100010, 2):
    if  num > sosu_2[sosu_2_index-1]:
        sosu_2_index += 1
    flag =  True
    for i in range(1,sosu_2_index):
        if num % sosu[i] == 0:
            flag = False
            break
    if flag:
        sosu.append(num)
        if num >= A:
            print(num)
            exit()
        sosu_2.append(num**2)