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

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
#include <bits/stdc++.h>
using namespace std;
int n;
int a[5][101][101];
int sd[5][3];
int main() {
  scanf("%d", &n);
  for (int t = 1; t <= 4; t++) {
    char ss[101];
    for (int i = 1; i <= n; i++) {
      scanf("%s", ss + 1);
      for (int j = 1; j <= n; j++) {
        int f = ss[j] - '0';
        a[t][i][j] = f;
      }
    }
  }
  for (int t = 1; t <= 4; t++) {
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) {
        if (((i - 1) * n + j) % 2 == 1 && a[t][i][j] == 0) sd[t][1]++;
        if (((i - 1) * n + j) % 2 == 0 && a[t][i][j] == 1) sd[t][1]++;
        if (((i - 1) * n + j) % 2 == 1 && a[t][i][j] == 1) sd[t][2]++;
        if (((i - 1) * n + j) % 2 == 0 && a[t][i][j] == 0) sd[t][2]++;
      }
  }
  int ans = 1e9;
  if (sd[1][1] + sd[2][1] + sd[3][2] + sd[4][2] < ans)
    ans = sd[1][1] + sd[2][1] + sd[3][2] + sd[4][2];
  if (sd[1][1] + sd[3][1] + sd[2][2] + sd[4][2] < ans)
    ans = sd[1][1] + sd[3][1] + sd[2][2] + sd[4][2];
  if (sd[1][1] + sd[4][1] + sd[3][2] + sd[2][2] < ans)
    ans = sd[1][1] + sd[4][1] + sd[3][2] + sd[2][2];
  if (sd[1][2] + sd[2][2] + sd[3][1] + sd[4][1] < ans)
    ans = sd[1][2] + sd[2][2] + sd[3][1] + sd[4][1];
  if (sd[1][2] + sd[3][2] + sd[2][1] + sd[4][1] < ans)
    ans = sd[1][2] + sd[3][2] + sd[2][1] + sd[4][1];
  if (sd[1][2] + sd[4][2] + sd[3][1] + sd[2][1] < ans)
    ans = sd[1][2] + sd[4][2] + sd[3][1] + sd[2][1];
  printf("%d", ans);
  return 0;
}
