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;
char p1[105][105];
char p2[105][105];
char p3[105][105];
char p4[105][105];
int c1[2], c2[2], c3[2], c4[2];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p1[i][j];
      if ((i + j) % 2 == 0 and p1[i][j] == '0')
        c1[0]++;
      else if ((i + j) % 2 and p1[i][j] == '1')
        c1[0]++;
      else
        c1[1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p2[i][j];
      if ((i + j) % 2 == 0 and p2[i][j] == '0')
        c2[0]++;
      else if ((i + j) % 2 and p2[i][j] == '1')
        c2[0]++;
      else
        c2[1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p3[i][j];
      if ((i + j) % 2 == 0 and p3[i][j] == '0')
        c3[0]++;
      else if ((i + j) % 2 and p3[i][j] == '1')
        c3[0]++;
      else
        c3[1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> p4[i][j];
      if ((i + j) % 2 == 0 and p4[i][j] == '0')
        c4[0]++;
      else if ((i + j) % 2 and p4[i][j] == '1')
        c4[0]++;
      else
        c4[1]++;
    }
  }
  int mi =
      min(min(c1[0] + c2[0] + c3[1] + c4[1], c1[0] + c3[0] + c2[1] + c4[1]),
          c1[0] + c4[0] + c3[1] + c2[1]);
  mi =
      min(min(min(c1[1] + c2[1] + c3[0] + c4[0], c1[1] + c3[1] + c2[0] + c4[0]),
              c1[1] + c4[1] + c3[0] + c2[0]),
          mi);
  cout << mi;
}
