Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_macros)]
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)*}
    };
}

#[allow(unused_macros)]
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)*}
    };
}

#[allow(unused_macros)]
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<_>>()
    };

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

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

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::HashSet;
use std::iter::FromIterator;

fn enum_primes(n: u64) -> Vec<u64>{
    let mut primes = vec![];
    let mut is_prime = vec![true; n as usize + 1];

    is_prime[0] = false;
    is_prime[1] = false;

    for i in 2..n as usize {
        if is_prime[i] == true {
            primes.push(i as u64);
            let mut j = 2;
            while (i*j) as u64 <= n {
                is_prime[i*j] = false;
                j += 1;
            }
        }
    }
    return primes;
}

fn main() {
    input!{
      n: usize,
    }
    let primes = enum_primes(55556*5);
    let primes_set: HashSet<u64> = HashSet::from_iter(primes.clone());

    let mut prime_idx = 6;
    let mut ans = vec![2, 3, 5, 7, 13];
    let mut combi = [0; 4];

    for i in 6..(n+1) as u64 {
        let bit = 1 << i-1;

        loop {
            if prime_idx >= primes.len() {
                println!("Couldn't find answer {}", n);
                return;
            }
            let prime = primes[prime_idx];
            let mut ok = true;
            for j in 1u64..bit {
                if j.count_ones() != 4 { continue; }
                let mut idx = 0;
                for k in 0..i {
                    if j & (1 << k) > 0 {
                        combi[idx] = ans[k as usize];
                        idx += 1;
                    }
                }

                let mut sum = prime;
                for v in &combi {
                    sum += *v;
                }
                if primes_set.contains(&sum) {
                    ok = false;
                    break;
                }
            }

            prime_idx += 1;
            if ok {
                ans.push(prime);
                break;
            }
        }
    }
    for i in 0..ans.len() {
        if i == ans.len() - 1 {
            print!("{}", ans[i]);
        } else {
            print!("{} ", ans[i]);
        }
    }
    println!();
}