Flood Fill

Two black and white images $A$ and $B$ of size $N \times M$ are given.

The flood fill tool works as follows. You choose any cell $(x, y)$, find its connected component, and flip the colors of all cells in that component: black cells become white, and white cells become black. The connected component of a cell is the set of cells you can reach by moving up, down, left, or right without changing color.

You can apply the flood fill tool to image $A$ any number of times. Find the minimum possible number of cells where $A$ differs from $B$ after some sequence of operations.

The first line contains two integers $N$ and $M$ ($1 \le N, M \le 100$), the dimensions of the images. Each of the next $N$ lines contains a binary string of length $M$ describing the corresponding row of image $A$. Each of the following $N$ lines contains a binary string of length $M$ describing the corresponding row of image $B$. 0 is a white cell and 1 is a black cell.

Output a single integer, the minimum possible number of cells where $A$ differs from $B$ after some sequence of operations.

In the first example, you can apply the tool to the middle cell twice. This way, the two images differ in only 1 cell.

In the second example, you can make the entire image black. This way, the two images differ in 7 cells.