Alice has an $m \times n$ grid, with rows numbered from $1$ to $m$ from top to bottom and columns numbered from $1$ to $n$ from left to right. The cell at the intersection of row $i$ ($1 \leq i \leq m$) and column $j$ ($1 \leq j \leq n$) is called cell $(i, j)$. Initially, the entire grid is white (color $0$). Alice performs $k$ coloring operations as follows:
- She selects a rectangle within the grid, covering a contiguous set of cells, and chooses a color $c$ ($1 \leq c \leq 30$);
- She then overwrites all cells within the selected rectangle to color $c$.
After performing $k$ operations, Alice obtains a colored grid. Bob also wants to recreate Alice's colored grid but does not know the operations she used. Since this is challenging, Bob aims to use no more than $h$ operations to make his grid resemble Alice's as closely as possible.
**Objective:** Given Alice's colored grid and the integer $k$, help Bob find a sequence of no more than $h$ operations to make his grid as similar to Alice's as possible.
### Input
- The first line contains three integers $m$, $n$, and $k$ ($k \leq 100$);
- Each of the next $m$ lines contains $n$ integers $a_{i1}, a_{i2}, \ldots, a_{in}$ describing the colors in row $i$ of Alice's color grid.
### Output
- The first line should contain a non-negative integer $h$ ($h \leq k$);
- Each of the next $h$ lines should contain five integers $x_s, y_s, u_s, v_s, c_s$, where $(x_s, y_s)$ and $(u_s, v_s)$ are the top-left and bottom-right corners of the rectangle chosen in the $s$-th coloring operation, and $c_s$ is the color for that rectangle.
### Constraints
- 30% of the tests (worth 30% of points) have $m, n, k \leq 5$;
- 50% of the tests (worth 50% of points) have $m, n \leq 50$;
- 20% of the tests (worth 20% of points) have $m, n \leq 500$.
### Scoring
There are 20 tests, each worth 5.0 points. Let $d$ be the number of cells in the generated grid that match Alice's grid. The score for each test is calculated as $5.0 \times \left( \frac{d}{m \times n} \right)^5$.
### Example
Input:
```
3 3 2
2 2 0
2 2 1
0 1 1
```
Output:
```
2
1 1 2 2 2
2 2 3 3 1
```
Alice's color grid:
| | | |
|---|---|---|
| 2 | 2 | 0 |
| 2 | 2 | 1 |
| 0 | 1 | 1 |
Bob's color grid:
| | | |
|---|---|---|
| 2 | 2 | 0 |
| 2 | 2 | 1 |
| 0 | 1 | 1 |
With this coloring strategy, a score of $5.0 \times \left( \frac{8}{9} \right)^5$ is achieved.
