You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
An $$$n \times m$$$ grid of characters is called great if it satisfies these three conditions:

- Each character is either 'A', 'B', or 'C'.
- Every $$$2 \times 2$$$ contiguous subgrid contains all three different letters.
- Any two cells that share a common edge contain different letters.

Let $$$(x,y)$$$ denote the cell in the $$$x$$$-th row from the top and $$$y$$$-th column from the left.

You want to construct a great grid that satisfies $$$k$$$ constraints. Each constraint consists of two cells, $$$(x_{i,1},y_{i,1})$$$ and $$$(x_{i,2},y_{i,2})$$$, that share exactly one corner. You want your great grid to have the same letter in cells $$$(x_{i,1},y_{i,1})$$$ and $$$(x_{i,2},y_{i,2})$$$.

Determine whether there exists a great grid satisfying all the constraints.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). The description of the test cases follows.

The first line of each test case contains three integers, $$$n$$$, $$$m$$$, and $$$k$$$ ($$$2 \le n,m \le 2 \cdot 10^3$$$, $$$1 \le k \le 4 \cdot 10^3$$$).

Each of the next $$$k$$$ lines contains four integers, $$$x_{i,1}$$$, $$$y_{i,1}$$$, $$$x_{i,2}$$$, and $$$y_{i,2}$$$ ($$$1 \le x_{i,1} < x_{i,2} \le n$$$, $$$1 \le y_{i,1},y_{i,2} \le m$$$). It is guaranteed that either $$$(x_{i,2},y_{i,2}) = (x_{i,1}+1,y_{i,1}+1)$$$ or $$$(x_{i,2},y_{i,2}) = (x_{i,1}+1,y_{i,1}-1)$$$.

The pairs of cells are pairwise distinct, i.e. for all $$$1 \le i < j \le k$$$, it is not true that $$$x_{i,1} = x_{j,1}$$$, $$$y_{i,1} = y_{j,1}$$$, $$$x_{i,2} = x_{j,2}$$$, and $$$y_{i,2} = y_{j,2}$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^3$$$.

It is guaranteed that the sum of $$$m$$$ over all test cases does not exceed $$$2 \cdot 10^3$$$.

It is guaranteed that the sum of $$$k$$$ over all test cases does not exceed $$$4 \cdot 10^3$$$.

## Output Format
For each test case, output "YES" if a great grid satisfying all the constraints exists and "NO" otherwise.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

## Examples
```input
4
3 4 4
1 1 2 2
2 1 3 2
1 4 2 3
2 3 3 2
2 7 2
1 1 2 2
1 2 2 1
8 5 4
1 2 2 1
1 5 2 4
7 1 8 2
7 4 8 5
8 5 4
1 2 2 1
1 5 2 4
7 1 8 2
7 5 8 4
```
```output
YES
NO
YES
NO
```

## Note
In the first test case, the following great grid satisfies all the constraints: BABCCBCAACAB

In the second test case, the two constraints imply that cells $$$(1,1)$$$ and $$$(2,2)$$$ have the same letter and cells $$$(1,2)$$$ and $$$(2,1)$$$ have the same letter, which makes it impossible for the only $$$2 \times 2$$$ subgrid to contain all three different letters.

Now solve the problem and return the code.