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 Rust (1.15.1) (judge verdict: Accepted)

use std::vec::Vec;
use std::collections::HashMap;
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

fn main() {
    let mut x: usize = read();
    let mut ans = 0;
    while true {
      let hash = trial_division(x);
      if hash.len() == 1 {
        let count = hash.iter().fold(0, |acc, (&key, &val)| acc + val);
        ans = x;
        if count == 1 {
          break
        }
      }
      x += 1;
    }
    println!("{}", x);
}

// 試し割り
// O(√N)
fn trial_division(n :usize) -> HashMap<usize, usize>{
    let mut primes = HashMap::new();
    let mut i = 2;
    let mut n = n;

    //  n を root n 以下の整数で割り切れるまで割っていく
    while i * i <= n {
        while n % i == 0 {
            n /= i;
            // match primes.get_mut(&i) {
            //   None => { primes.insert(i, 1); },
            //   Some(x) => {
            //       *x += 1;
            //   },
            // }

            match primes.get(&i) {
              Some(&val) => {
                primes.insert(i, val + 1);
              },
              _  => { primes.insert(i, 1); },
            }
        }
        i+=1;
    }

    // 最後にnが素数になっている場合はそれ自身も素因数に含めて終了
    // match primes.get_mut(&n) {
    //   None => { primes.insert(n, 1); },
    //   Some(x) => {
    //     *x += 1;
    //   },
    // }

     match primes.get(&n) {
          Some(&val) => {
            primes.insert(n, val + 1);
          },
          _  => { primes.insert(n, 1); },
      }

    primes
}