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 (3.8.2) (judge verdict: Wrong Answer)

import math

X = int(input())

l = [True] * 1000001
l[0], l[0] = False, False

for i in range(1, 1000+1):
  if l[i]:
    if i >= X:
      print(i)
      break
    else:
      for j in range(2*i, 1000000, i):
        l[j] = False