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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
mod prime {
    pub fn is_prime(n: usize) -> bool {
        match n {
            0 | 1 => false,
            2 => true,
            _ => {
                if n % 2 == 0 {
                    return false;
                }
                let mut i = 3;
                while i <= (n as f64).sqrt() as usize + 1 {
                    if n % i == 0 {
                        return false;
                    }
                    i += 2;
                }
                true
            }
        }
    }
    pub fn prime_all(n: usize) -> Vec<usize> {
        let mut list = Vec::new();
        list.push(2);
        for i in 3..n + 1 {
            let mut flg = false;
            for j in &list {
                if i % j == 0 {
                    flg=true;
                    break; 
                }
                if i < j*j {
                    break;
                }
            }
            if !flg {
                list.push(i);
            }
        }
        list
    }

    pub fn factorize(mut n: usize) -> Vec<(usize, usize)> {
        let mut list = Vec::new();
        if is_prime(n) {
            list.push((n, 1));
            return list;
        }
        let primes = prime_all((n as f64).sqrt() as usize + 1);
        for x in &primes {
            let x = *x;
            if n % x != 0 {
                continue;
            }
            list.push((x, 0_usize));
            while n % x == 0 {
                n /= x;
                let index = list.len() - 1;
                list[index].1 += 1;
            }
            if is_prime(n) {
                list.push((n, 1));
                break;
            }
        }
        list
    }
}

fn main() {
    input!(x:i32);
    for i in x.. {
        if prime::is_prime(i as usize) {
            println!("{}",i);
            return;
        }
    }
}