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 true_1[201][201], true_2[201][201];
int A[101][101][4];
int main() {
  int n, Min = 1e9;
  cin >> n;
  for (int k = 0; k < 4; k++)
    for (int i = 0; i < n; i++, cout << endl)
      for (int j = 0; j < n; j++) {
        char s;
        cin >> s;
        A[i][j][k] = s - '0';
      }
  for (int i = 0; i < 200; i++, cout << endl)
    for (int j = 0; j < 200; j++) {
      true_1[i][j] = ((i + j) & 1);
      true_2[i][j] = !((i + j) & 1);
    }
  int p[4] = {0, 1, 2, 3};
  do {
    int E[201][201];
    int i, ii;
    for (i = 0; i < n; i++) {
      int j;
      for (j = 0; j < n; j++) {
        E[i][j] = A[i][j][p[0]];
      }
      int jj;
      for (j = n, jj = 0; j < 2 * n; j++, jj++) {
        E[i][j] = A[i][jj][p[1]];
      }
    }
    for (i = n, ii = 0; i < 2 * n; i++, ii++) {
      int j;
      for (j = 0; j < n; j++) {
        E[i][j] = A[ii][j][p[2]];
      }
      int jj;
      for (j = n, jj = 0; j < 2 * n; j++, jj++) {
        E[i][j] = A[ii][jj][p[3]];
      }
    }
    int cnt1 = 0, cnt2 = 0;
    for (int i = 0; i < 2 * n; i++, cout << endl) {
      for (int j = 0; j < 2 * n; j++) {
        if (E[i][j] != true_1[i][j]) {
          cnt1++;
        }
        if (E[i][j] != true_2[i][j]) {
          cnt2++;
        }
      }
    }
    Min = min(cnt1, min(cnt2, Min));
  } while (next_permutation(p, p + 4));
  cout << Min << endl;
}
