Problem E
Hair Pattern
When Skimpy grooms himself he can do vertical or horizontal strokes that covers his entire chest.
We can think of Skimpy chest as a grid with $N$ rows of $M$ squares each, and in one movement he can make an entire column or an entire row black or white.
Skimpy has a desired pattern he wants to achieve. He wants you to help him to get as close as possible to such pattern. You are to write a program to determine the maximum number of grid squares that can be identical to the pattern. See the samples below.
Input
The first line of input contains two integers $N$ and $M$ ($1 \le N, M \le 8$), the number of rows and columns of the grid on Skimpy’s chest.
The next $N$ lines contains $M$ characters each, either ’B’ representing a black spot, or ’W’ representing a white spot. This represents the current pattern on Skimpy’s chest.
The next $N$ lines represents another grid in the same format, but with Skimpy’s desired pattern.
Output
The output should contain a single integer representing the maximum number of grid squares that Skimpy can satisfy.
Explanation
On the first sample below, Skimpy’s initial pattern is only one square of the desired pattern, and there is nothing he can do to get that one square right without making even more squares wrong. So he can match at most $8$ of the $9$ squares.
On the second sample Skimpy can achieve the desired pattern by: making the second row black, then the third column white, then the first column black. He can match all $9$ grid squares.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 3 WWW WBW WWW BWW WBW WWW |
8 |
| Sample Input 2 | Sample Output 2 |
|---|---|
3 3 WWW WWW WWW BWW BBW BWW |
9 |
| Sample Input 3 | Sample Output 3 |
|---|---|
3 3 WWW WBW WWW BWB WBW BWB |
8 |
| Sample Input 4 | Sample Output 4 |
|---|---|
3 3 WWW WWW WWW WWW WBW WWW |
9 |
| Sample Input 5 | Sample Output 5 |
|---|---|
3 3 BBB BBB BBB BWB WBW BWB |
8 |
| Sample Input 6 | Sample Output 6 |
|---|---|
3 3 BWB BWB BWB WWW BBB WWW |
9 |
