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;
const int inf = 0x3f3f3f3f;
char mp[110][110];
int ans[5][2];
int vis[10];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      scanf("%s", mp[j] + 1);
    }
    int ans1 = 0, ans2 = 0;
    for (int j = 1; j <= n; j++) {
      for (int k = 1; k <= n; k++) {
        if ((k + j) % 2 == 0 && mp[j][k] == '0') ans1++;
        if ((k + j) % 2 == 0 && mp[j][k] == '1') ans2++;
        if ((k + j) % 2 == 1 && mp[j][k] == '1') ans1++;
        if ((k + j) % 2 == 1 && mp[j][k] == '0') ans2++;
      }
    }
    ans[i][0] = ans1;
    ans[i][1] = ans2;
  }
  int ret = inf;
  for (int i = 1; i <= 4; i++) {
    for (int j = i + 1; j <= 4; j++) {
      memset(vis, 0, sizeof(vis));
      vis[i] = 1;
      vis[j] = 1;
      int tmp = ans[i][0] + ans[j][0];
      for (int k = 1; k <= 4; k++)
        if (!vis[k]) tmp += ans[k][1];
      ret = min(ret, tmp);
    }
  }
  printf("%d\n", ret);
  return 0;
}
