Largest Square

There is an $N \times N$ mosaic of square solar cells ($1 \le N \le 2000$). Each solar cell is either good or bad. There are $W$ bad cells ($1 \le W \le 50000$). You must find the largest square within the mosaic that contains at most $L$ ($0 \le L \le W$) bad cells.

The first line of input contains a single integer $Z$ ($Z \le 20$), the number of test cases. The $Z$ test cases then follow.

The first line of a test case contains three space-separated integers $N$, $W$, and $L$. The next $W$ lines each contain two space-separated integers giving the row and column (each from $1$ to $N$) of a bad solar cell.

For each input instance, output a single integer: the area of the largest square that contains no more than $L$ bad solar cells.

Suppose the mosaic is $4 \times 4$ with the following arrangement of good ('G') and bad ('B') cells:

BGGG
GBBG
GGGG
GGGG

Several $2 \times 2$ squares near the bottom contain no bad cells, but every $3 \times 3$ square contains at least two bad cells.