A11721. Chessboard

Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into $4$ pieces, each of size $n$ by $n$ , $n$ is always odd. And what's even worse, some squares were of wrong color. $j$ -th square of the $i$ -th row of $k$ -th piece of the board has color $a_{k,i,j}$ ; $1$ being black and $0$ being white.

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be $2n$ by $2n$ . You are allowed to move pieces but not allowed to rotate or flip them.

The first line contains odd integer $n$ $(1<=n<=100)$ — the size of all pieces of the board.

Then $4$ segments follow, each describes one piece of the board. Each consists of $n$ lines of $n$ characters; $j$ -th one of $i$ -th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.