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.

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 nlines 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

10010

Output

1

Input

3101010101101000101010101011010101010

Output

2

题解：

#include 
    
     #include
     
      #include
      
       #include
       
        using namespace std;int n;char map[4][150][150];int move[4][2] = {1,0,0,1,-1,0,0,-1};int dfs_1(int q){	int count = 0;	if (map[q][0][0] == '0')	{	}	else	{		count++;	}	int p = 0;	for (int i = 0; i < n; i++)	{		for (int j = 0; j < n ; j++)		{			if (i == 0 && j == 0)			{				continue;			}			else			{				if (map[q][i][j]-'0' == !p)				{					p = map[q][i][j] - '0';				}				else				{					p = !p;					count++;				}			}		}	}	return count;}int dfs_2(int q){	int count = 0;	if (map[q][0][0] == '1')	{	}	else	{		count++;	}	int p = 1;	for (int i = 0; i < n; i++)	{		for (int j = 0; j < n ; j++)		{			if (i == 0 && j == 0)			{				continue;			}			else			{				if (map[q][i][j]-'0' == !p)				{					p = map[q][i][j] - '0';				}				else				{					p = !p;					count++;				}			}		}	}	return count;}int main(){	scanf("%d", &n);	for (int i = 0; i < 4; i++)	{		for (int j = 0; j < n; j++)		{			scanf("%s", map[i][j]);		}	}	int answer[4][2];	for (int i = 0; i < 4 ;i++)	{		answer[i][0] = dfs_1(i);		answer[i][1] = dfs_2(i);	}	int m = 100000000;	m = min(answer[0][0]+ answer[1][0]+answer[2][1]+answer[3][1], m);	m = min(answer[0][0]+ answer[1][1]+answer[2][0]+answer[3][1], m);	m = min(answer[0][0]+ answer[1][1]+answer[2][1]+answer[3][0], m);	m = min(answer[0][1]+ answer[1][1]+answer[2][0]+answer[3][0], m);	m = min(answer[0][1]+ answer[1][0]+answer[2][1]+answer[3][0], m);	m = min(answer[0][1]+ answer[1][0]+answer[2][0]+answer[3][1], m);	printf("%d\n", m);		return 0;}