Circuit Board

Arsh recently found an old rectangular circuit board that he would like to recycle. The board has $R$ rows and $C$ columns of squares. Each square has a thickness in millimetres. The square in row $r$ and column $c$ has thickness $V_{r,c}$.

A circuit board is good if in each row, the difference between the thickest square and the thinnest square is at most $K$. The original board might not be good, so Arsh wants to find a good subcircuit board. A subcircuit board is an axis-aligned subrectangle of the original board.

Find the number of squares in the largest good subrectangle.

The first line contains $T$, the number of test cases. Each test case begins with a line containing $R$, $C$, and $K$. Then $R$ lines follow, each with $C$ integers. The $c$-th integer on the $r$-th line is $V_{r,c}$.

For each test case, output one line Case #x: y, where $x$ is the test case number starting from 1, and $y$ is the maximum number of squares in a good subrectangle.

$1 \le T \le 50$.

$1 \le R \le 300$.

$1 \le C \le 300$.

$0 \le V_{i,j} \le 10^3$ for all $i, j$.