White Lines

Gildong has bought a famous painting software cfpaint. The working screen of cfpaint is a square of $n$ rows and $n$ columns of cells. Rows are numbered 1 to $n$ from top to bottom, and columns are numbered 1 to $n$ from left to right. The cell at row $r$ and column $c$ is written $(r,c)$. Each cell is either black or white.

The eraser tool has an integer size $k$ ($1\le k\le n$). To use it, Gildong clicks a cell $(i,j)$ with $1\le i,j\le n-k+1$. Every cell $(i',j')$ with $i\le i'\le i+k-1$ and $j\le j'\le j+k-1$ becomes white. In other words, the square of side $k$ with top left corner $(i,j)$ is painted white.

A white line is a row or column with no black cells.

Gildong has used cfpaint for a while, so some cells (possibly none or all) are black now. Find the maximum number of white lines after using the eraser exactly once.

The first line has two integers $n$ and $k$ ($1\le k\le n\le 2000$), the number of rows and columns and the eraser size. The next $n$ lines each contain $n$ characters without spaces. The $j$-th character of the $i$-th line is the cell $(i,j)$: 'B' for black, 'W' for white.

Print one integer: the maximum number of white lines that can be obtained after using the eraser exactly once.

In the first example, Gildong can click cell $(2,2)$. The screen then becomes:

BWWW
WWWW
WWWW
WWWB

There are four white lines: rows 2 and 3, and columns 2 and 3.

In the second example, clicking cell $(2,3)$ makes row 2 a white line.

In the third example, clicking cell $(3,2)$ makes both column 2 and row 5 white lines.