Problem Statement

Construct a sequence of positive integers $A_1,A_2,...,A_{\left\lceil \frac{N}{2} \right\rceil}$ of length $\displaystyle \left\lceil \frac{N}{2} \right\rceil$ that satisfies the following conditions. If no sequence satisfying the conditions exists, report that fact.

• $1 \le A_i \le N$
• If $i \neq j$, then $A_i \neq A_j$
• $\mathrm{gcd}(A_i,A_{i+1}) \neq 1\ (1 \le i \le \displaystyle \left\lceil \frac{N}{2} \right\rceil -1)$

Here, $\displaystyle \lceil x \rceil$ denotes the smallest integer greater than or equal to the real number $x$.

Input

$N$

• All inputs are integers.
• $1 \le N \le 2 \times 10^5$

Output

If no sequence of positive integers satisfying the conditions exists, print $-1$.

If a sequence of positive integers satisfying the conditions exists, print such a sequence separated by spaces, as follows.

If there are multiple solutions, you may print any of them.

$A_1\ A_2\ \dots\ A_{\left\lceil \frac{N}{2} \right\rceil}$

Sample

11

3 9 6 2 10 5