For ibasic, who inherited the will of ian0704, let us find a sequence $A$ of length $3N$ that satisfies all of the following conditions:
- $A$ is a permutation containing each integer from $1$ to $3N$ exactly once.
- For all $l, r$ such that $1\le l< r\le 3N$, the median of $[A_l, A_{l+1}, \dots, A_r]$ is between $N+1$ and $2N$ inclusive. The median of a sequence of length $k$ is the $\frac{k+1}{2}$-th smallest number if $k$ is odd, and the average of the $\frac{k}{2}$-th smallest and $\frac{k}{2}+1$-th smallest numbers if $k$ is even.
Input
The first line contains an integer $N$.
Output
Output the sequence $A_1, A_2, \dots, A_{3N}$ satisfying the conditions, separated by spaces. If no such sequence exists, output -1 instead. If there are multiple possible sequences, any one of them is acceptable.
Examples
Input 1
2
Output 1
1 5 3 4 2 6