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There is an `N\ times\ N` mosaic of square solar cells (`1\ ≤\ N\ ≤\ 2\ 000`). Each solar cell is either good or bad. There are `W` (`1\ ≤\ W\ ≤\ 50\ 000`) bad cells. You need to find the largest square within the mosaic containing at most `L` (`0\ ≤\ L\ ≤\ W`) bad cells.

The input will begin with a number `Z\ ≤\ 20`, the number of test cases, on a line by itself. `Z` test cases then follow. The first line of the test case contains three space-separated integers: `N`, `W`, and `L`. `W` lines follow, each containing two space-separated integers representing the coordinates of a location of the bad solar cells.

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

1
4 3 1
1 1
2 2
2 3

4

The mosaic is `4\ times\ 4`, and contains the following arrangement of good and bad cells ('G' represents good, and 'B' represents bad):

BGGG
GBBG
GGGG
GGGG

Several `2\ times\ 2` squares at the bottom contain no bad solar cells, but all `3\ times\ 3` squares contain at least two bad solar cells.