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 main() {
  int N;
  cin >> N;
  int Mat[4][N][N];
  memset(Mat, 0, sizeof Mat);
  string str[4][N];
  for (int x = 0; x < 4; x++)
    for (int i = 0; i < N; i++) {
      cin >> str[x][i];
      for (int j = 0; j < N; j++) Mat[x][i][j] = (int)(str[x][i][j] - '0');
    }
  vector<int> A;
  A.push_back(0);
  A.push_back(1);
  A.push_back(2);
  A.push_back(3);
  int saida = 0x3f3f3f3f;
  int MatOT[2][2 * N][2 * N];
  for (int x = 0; x < 2; x++) {
    for (int i = 0; i < 2 * N; i++) {
      for (int j = 0; j < 2 * N; j++) {
        if (i == 0 and j == 0)
          MatOT[x][i][j] = x;
        else {
          if (j == 0) {
            MatOT[x][i][j] = !MatOT[x][i - 1][j];
          } else
            MatOT[x][i][j] = !MatOT[x][i][j - 1];
        }
      }
    }
  }
  do {
    for (int x = 0; x < 2; x++) {
      int cont = 0;
      for (int i = 0; i < 2 * N; i++) {
        for (int j = 0; j < 2 * N; j++) {
          if (i >= N and j >= N) {
            if (Mat[A[3]][i - N][j - N] != MatOT[x][i][j]) cont++;
          } else if (i >= N) {
            if (Mat[A[2]][i - N][j] != MatOT[x][i][j]) cont++;
          } else if (j >= N) {
            if (Mat[A[1]][i][j - N] != MatOT[x][i][j]) cont++;
          } else {
            if (Mat[A[0]][i][j] != MatOT[x][i][j]) cont++;
          }
        }
      }
      saida = min(saida, cont);
    }
  } while (next_permutation(A.begin(), A.end()));
  cout << saida << '\n';
}
