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.

3

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 $gcd(2, 4, 6) = 2 > 1$.

4

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.