Problem:
Score : 600 points

Problem Statement

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.

She thinks that a set S = \{a_{1}, a_{2}, ..., a_{N}\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.

Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.

Constraints

3 \leq N \leq 20000

Input

Input is given from Standard Input in the following format:

N

Output

Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :

The elements must be distinct positive integers not exceeding 30000.

The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.

S is a special set.

If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.

Sample Input 1

3

Sample Output 1

2 5 63

\{2, 5, 63\} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the criteria.

Note that \{2, 4, 6\} is not a valid solution because gcd(2, 4, 6) = 2 > 1.

Sample Input 2

4

Sample Output 2

2 5 20 63

\{2, 5, 20, 63\} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5, 20, 63) = 1. Thus, this set satisfies all the criteria.

Solution in PHP (5.6.30) (judge verdict: Runtime Error)

<?php

$stdins = [];
while($line=fgets(STDIN)){
    $stdins[] = trim($line);
}

$N = $stdins[0];
$Gs = [2];
for($i=3;$i<=30000;$i++){
    $found = false;
    $Fs = $Gs;
    $Gs[] = $i;
    foreach($Gs as $G) {
        $Hs = array_filter($Gs, function($p) use ($G){ return $p != $G; });
        $H = array_sum($Hs);
        if(gmp_gcd($G, $H) == 1){
            $found = true;
            break;
        }
    }
    if($found){
        $Gs = $Fs;
        continue;
    }

    $found = false;
    foreach($Gs as $G) {
        $Hs = array_filter($Gs, function($p) use ($G){ return $p != $G; });
        foreach($Hs as $H){
            if(gmp_gcd($G, $H) != 1){
                $found = true;
                break;
            }
        }
        if($found) break;
    }
    if($found){
        $Gs = $Fs;
        continue;
    }

    if(count($Gs) >= $N) break;
}
print(implode(" ", $Gs));