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 = 1e9;
int n;
int arr[5][110][110];
int cost[5][5];
int calc(int idx, int color) {
  int res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (arr[idx][i][j] != color) res++;
      color = 1 - color;
    }
  }
  return res;
}
int main() {
  memset(cost, 0, sizeof(cost));
  cin >> n;
  string s;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s;
      for (int k = 0; k < n; k++) {
        arr[i][j][k] = s[k] - '0';
      }
    }
  }
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 2; j++) {
      cost[i][j] = calc(i, j);
    }
  }
  int mini = INF;
  mini = min(mini, cost[0][0] + cost[1][0] + cost[2][1] + cost[3][1]);
  mini = min(mini, cost[0][0] + cost[1][1] + cost[2][0] + cost[3][1]);
  mini = min(mini, cost[0][0] + cost[1][1] + cost[2][1] + cost[3][0]);
  mini = min(mini, cost[0][1] + cost[1][0] + cost[2][0] + cost[3][1]);
  mini = min(mini, cost[0][1] + cost[1][0] + cost[2][1] + cost[3][0]);
  mini = min(mini, cost[0][1] + cost[1][1] + cost[2][0] + cost[3][0]);
  cout << mini << endl;
  return 0;
}
