Problem Statement

Mitaru City is a town that can be represented as an $H \times W$ grid. The cell in the $i$-th row from the top and the $j$-th column from the left is denoted by $(i,j)$.
Mitaru City has $N$ tourist attractions, and the $i$-th tourist attraction is located at $(x_i,y_i)$.

A sequence $T$ of positive integers of length $X$ is called a good journey if it satisfies the following conditions. Here, $T_i$ denotes the $i$-th term of $T$, and $T_{X+1}$ is regarded as $T_1$.

• $X \geq 4$
• $1 \leq T_i \leq N$ $(\ 1 \leq i \leq X\ )$
• $T_i \neq T_j$ $(\ i \neq j\ )$
• For every integer $i$ satisfying $1 \leq i \leq X$, the following holds.
• If $i$ is even, the $T_i$-th tourist attraction and the $T_{i+1}$-th tourist attraction are in the same row. That is, $x_{T_i}=x_{T_{i+1}}$ holds.
• If $i$ is odd, the $T_i$-th tourist attraction and the $T_{i+1}$-th tourist attraction are in the same column. That is, $y_{T_i}=y_{T_{i+1}}$ holds.

Determine whether a good journey exists, and if it does, show $1$ of them.

Input

$H\ \ W\ \ N$
$x_1\ \ y_1$
$x_2\ \ y_2$
$\vdots$
$x_N\ \ y_N$

• $2 \leq H,W \leq 10^5$
• $4 \leq N \leq \mathrm{min}(H \times W,10^5)$
• $1 \leq x_i \leq H$ ( $1 \leq i \leq N$ )
• $1 \leq y_i \leq W$ ( $1 \leq i \leq N$ )
• $(x_i,y_i)$ are pairwise distinct
• All inputs are integers

Output

If no good journey exists, output -1 followed by a newline.
If one exists, output $1$ of them in the following format. If there are multiple solutions, you may output any of them.

$X$
$T_1\ \ T_2\ \ \cdots T_X$

Sample

2 2 4
1 1
1 2
2 1
2 2

4
1 3 4 2

4
4 2 1 3

3 3 4
1 1
2 2
3 3
1 3

-1

4 4 8
1 1
3 1
3 3
2 3
2 2
4 2
4 4
1 4

8
1 2 3 4 5 6 7 8