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문제

There is an N × 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.

입력

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.

출력

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.

예제 입력

1
4 3 1
1 1
2 2
2 3

예제 출력

4

힌트

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

BGGG
GBBG
GGGG
GGGG

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