C. Chessboard time limit per test1 second memory limit per test256 megabytes inputstandard input out

C. Chessboard

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 ak, 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.

Input

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.

Output

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

Examples

input

Copy

1
0

0

1

0

output

1

input

Copy

3
101
010
101

101
000
101

010
101
011

010
101
010

output

2

这个题感觉蛮有意思，四块棋盘，每个格子或者是0或者是1，让你把四个长为奇数的棋盘合成一个棋盘，顺序不计，问你最少1修改几个格子，使得每个格子与相邻的格子数字不同。

我们先想想，正确的棋盘是什么样子那？ 无非是1个0,1个1交替出现，与坐标联系起来，i+j 为奇数则为 某个状态，否则为另一个状态。其实一个完整的棋盘分成四个，再把它合起来，能产生两种棋盘，第一个为0 或者第一个为 1.

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