CF1404E.Bricks

A brick is defined as a rectangle with integer side lengths with either width $1$ or height $1$ (or both).

There is an $n\times m$ grid, and each cell is colored either black or white. A tiling is a way to place bricks onto the grid such that each black cell is covered by exactly one brick, and each white cell is not covered by any brick. In other words, bricks are placed on black cells only, cover all black cells, and no two bricks overlap.

An example tiling of the first test case using $5$ bricks. It is possible to do better, using only $4$ bricks. What is the minimum number of bricks required to make a valid tiling?

The first line contains two integers $n$ , $m$ ( $1\le n, m\le 200$ ) — the number of rows and columns, respectively.

The next $n$ lines describe the grid. The $i$ -th of these lines contains a string of length $m$ , where the $j$ -th character denotes the color of the cell in row $i$ , column $j$ . A black cell is given by "#", and a white cell is given by ".".

It is guaranteed that there is at least one black cell.

Output a single integer, the minimum number of bricks required.

The first test case can be tiled with $4$ bricks placed vertically.

The third test case can be tiled with $18$ bricks like this: