There is a grid with $H$ rows and $W$ columns. Initially, all cells are painted with color $0$.

You will perform the following operations in the order $i = 1, 2, \ldots, M$.

-   If $T_i = 1$, repaint all cells in the $A_i$-th row with color $X_i$.
    
-   If $T_i = 2$, repaint all cells in the $A_i$-th column with color $X_i$.
    
After all operations are completed, for each color $i$ that exists on the grid, find the number of cells that are painted with color $i$.

The input is given from Standard Input in the following format:

```
$H$ $W$ $M$
$T_1$ $A_1$ $X_1$
$T_2$ $A_2$ $X_2$
$\vdots$
$T_M$ $A_M$ $X_M$
```

Let $K$ be the number of distinct integers $i$ such that there are cells painted with color $i$. Print $K + 1$ lines.

The first line should contain the value of $K$.

The second and subsequent lines should contain, for each color $i$ that exists on the grid, the color number $i$ and the number of cells painted with that color.

Specifically, the $(i + 1)$-th line $(1 \leq i \leq K)$ should contain the color number $c_i$ and the number of cells $x_i$ painted with color $c_i$, in this order, separated by a space.

Here, print the color numbers in ascending order. That is, ensure that $c_1 < c_2 < \ldots < c_K$. Note also that $x_i > 0$ is required.

-   $1 \leq H, W, M \leq 2 \times 10^5$
-   $T_i \in \lbrace 1, 2 \rbrace$
-   $1 \leq A_i \leq H$ for each $i$ such that $T_i = 1$,
-   $1 \leq A_i \leq W$ for each $i$ such that $T_i = 2$.
-   $0 \leq X_i \leq 2 \times 10^5$
-   All input values are integers.

3
0 5
2 4
5 3

The operations will change the colors of the cells in the grid as follows:

0000   0000   0000   0000   0000
0000 → 5555 → 5550 → 5550 → 5550 
0000   0000   0000   3333   2222

Eventually, there are five cells painted with color 0, four with color 2, and three with color 5.