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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $n);

$start = [2, 3, 25];
$pairs = [
	[30, 60],
	[32, 28],
	[33, 27],
	[4, 26],
	[5, 55],
	[6, 24],
	[8, 22],
	[9, 21],
	[10, 20],
	[12, 18],
	[14, 16],
];

if ($n == 3) {
	echoes($start);
	return;
}

if (($n % 2) === 0) {
	$start[] = 30;
}

if ($n == 4) {
	echoes($start);
	return;
}

$times = ($n - count($start)) / 2;
$alpha = 0;
while (true) {
	foreach ($pairs as $pair) {
		if (($alpha % 2 == 0) && $pair[0] === 30) {
			continue;
		}
		$start[] = $pair[0] + 30 * $alpha;
		$start[] = $pair[1] + 30 * $alpha;
		$times--;
		if ($times === 0) {
			break 2;
		}
	}
	$alpha++;
}
echoes($start);
return;

function echoes(array $a) {
	foreach ($a as $value) {
		echo $value, " ";
	}
	echo "\n";
}