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: Accepted)

//! https://github.com/hatoo/competitive-rust-snippets
//!
//! MIT License
//!
//! Copyright (c) 2018 hatoo
//!
//! Permission is hereby granted, free of charge, to any person obtaining a copy
//! of this software and associated documentation files (the "Software"), to deal
//! in the Software without restriction, including without limitation the rights
//! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//! copies of the Software, and to permit persons to whom the Software is
//! furnished to do so, subject to the following conditions:
//!
//! The above copyright notice and this permission notice shall be included in all
//! copies or substantial portions of the Software.
//!
//! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
//! SOFTWARE.
#![allow(
    unused_imports,
    unused_attributes,
    unused_macros,
    dead_code,
    non_snake_case
)]
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{stdin, stdout, BufWriter, Write};
use std::iter::FromIterator;
#[macro_export]
macro_rules !get {(@inner [$src :expr ] chars ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .chars () .collect ::<Vec <char >>() } } ;(@inner [$src :expr ] usize1 ) =>{{get !(@inner [$src ] usize ) -1 } } ;(@inner [$src :expr ] [usize1 ] ) =>{{get !(@inner [$src ] [usize ] ) .into_iter () .map (|v |v -1 ) .collect ::<Vec <usize >>() } } ;(@inner [$src :expr ] [[usize1 ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [usize1 ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[chars ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [chars ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [($($tt :tt ) ,*) ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] ($($tt ) ,*) ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] ($($tt :tt ) ,*) ) =>{{let mut buf :String =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;let mut iter =buf .split_whitespace () ;($(get !(@inner_elem_parse [$tt ] iter .next () .unwrap () ) ,) *) } } ;(@inner [$src :expr ] [$t :ty ] ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .map (|t |t .parse ::<$t >() .unwrap () ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[$t :ty ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [$t :ty ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] $t :ty ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .next () .unwrap () .parse ::<$t >() .unwrap () } } ;(@inner_elem_parse [usize1 ] $elem :expr ) =>{{get !(@inner_elem_parse [usize ] $elem ) -1 } } ;(@inner_elem_parse [$t :ty ] $elem :expr ) =>{{$elem .parse ::<$t >() .unwrap () } } ;($tt :tt ) =>{{use std ::io ::BufRead ;let get_stdin =std ::io ::stdin () ;let mut locked_stdin =get_stdin .lock () ;get !(@inner [&mut locked_stdin ] $tt ) } } ;}
macro_rules !debug {($($a :expr ) ,*$(,) *) =>{#[cfg (debug_assertions ) ] eprintln !(concat !($("| " ,stringify !($a ) ,"={:?} " ) ,*,"|" ) ,$(&$a ) ,*) ;} ;}
macro_rules !echo {($($a :expr ) ,*) =>{let mut s =Vec ::new () ;$(s .push (format !("{}" ,$a ) ) ;) *println !("{}" ,s .join (" " ) ) ;} }
#[macro_export]
macro_rules !chmin {($base :ident ,$($cmps :expr ) ,+$(,) *) =>{$base =min !($base ,$($cmps ) ,+) ;} ;}
#[macro_export]
macro_rules !chmax {($base :ident ,$($cmps :expr ) ,+$(,) *) =>{$base =max !($base ,$($cmps ) ,+) ;} ;}
#[macro_export]
macro_rules !min {($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::min ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::min ($a ,min !($($rest ) ,+) ) } } ;}
#[macro_export]
macro_rules !max {($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::max ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::max ($a ,max !($($rest ) ,+) ) } } ;}
const BIG_STACK_SIZE: bool = true;
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    let N = get!(usize);
    let primes: Vec<_> = 55555
        .lower_primes()
        .into_iter()
        .filter_map(|x| {
            if x % 5 == 1 {
                Some(x.to_string())
            } else {
                None
            }
        })
        .take(N)
        .collect();
    echo!(primes.join(" "));
}

pub trait Int:
    std::ops::Add<Output = Self>
    + std::ops::Sub<Output = Self>
    + std::ops::Mul<Output = Self>
    + std::ops::Div<Output = Self>
    + std::ops::Rem<Output = Self>
    + std::hash::Hash
    + PartialEq
    + Eq
    + PartialOrd
    + Ord
    + Copy
{
    fn zero() -> Self;
    fn one() -> Self;
    fn next(self) -> Self;
    fn prev(self) -> Self;
    fn sqrt_floor(self) -> Self;
}
macro_rules !impl_int_for_numerics {($($t :ty ) *) =>($(impl Int for $t {fn zero () ->Self {0 } fn one () ->Self {1 } fn next (self ) ->Self {self +Self ::one () } fn prev (self ) ->Self {self -Self ::one () } fn sqrt_floor (self ) ->Self {if self <Self ::zero () {return Self ::zero () ;} let two =Self ::one () .next () ;let mut ok =Self ::zero () ;let mut ng =self .next () ;while ng -ok >1 {let mid =(ng +ok ) /two ;if mid *mid <=self {ok =mid ;} else {ng =mid ;} } ok } } ) *) }
impl_int_for_numerics !(u8 i8 u16 i16 u32 i32 u64 i64 usize isize );
pub trait Prime<T: Int> {
    fn lower_primes(&self) -> Vec<T>;
    fn factorize(&self) -> std::collections::HashMap<T, usize>;
}
impl<T> Prime<T> for T
where
    T: Int,
{
    /// エラトステネスの篩を用いてself以下の素数を求める
    /// 計算量: O(n log log n)
    fn lower_primes(&self) -> Vec<T> {
        let &this = self;
        let mut v = Vec::new();
        if this <= T::one() {
            return v;
        }
        let mut deque = std::collections::VecDeque::new();
        let mut t = T::one().next();
        while t <= this {
            deque.push_back(t);
            t = t.next();
        }
        let mut p = match deque.pop_front() {
            Some(x) => x,
            None => return v,
        };
        v.push(p);
        while p * p <= this {
            deque = deque
                .iter()
                .filter(|&&x| x % p != T::zero())
                .cloned()
                .collect();
            p = match deque.pop_front() {
                Some(x) => x,
                None => return v,
            };
            v.push(p);
        }
        for n in deque {
            v.push(n);
        }
        v
    }
    /// エラトステネスの篩を用いてselfを素因数分解する
    fn factorize(&self) -> std::collections::HashMap<T, usize> {
        let mut ret = std::collections::HashMap::new();
        let primes = self.sqrt_floor().lower_primes();
        let mut tmp = *self;
        for prime in primes {
            while tmp % prime == T::zero() {
                tmp = tmp / prime;
                *ret.entry(prime).or_insert(0) += 1;
            }
        }
        if tmp > T::one() {
            *ret.entry(tmp).or_insert(0) += 1;
        }
        ret
    }
}