Problem F
LED Game
You are given two $n$ by $n$ boards of LED lights, each light is either off or on (represented by $0$ and $1$ respectively).
Next to each row, and above each column of each board is a button “flip”, which, for every LED in that row or column, turns that LED from off to on or on to off.
Determine the maximum number of LEDs you can get to match on the two boards.
Input
The first line of input is an integer $n$, where $1 \leq n \leq 14$.
The first $n$ lines of input are length-$n$ strings of $0$s and $1$s, where $0$ indicates that the corresponding light is off, and $1$ indicates that it is on. These $n$ lines represent the first board.
The next $n$ lines are length-$n$ strings of $0$s and $1$s. These $n$ lines represent the second board.
Output
Output the maximum number of LEDs you can get to match on the two boards.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 10 01 00 00 |
4 |
| Sample Input 2 | Sample Output 2 |
|---|---|
3 000 100 100 111 111 111 |
8 |
