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 mat[4][105][105];
int main() {
  long long n, minsol = 5445242543543;
  cin >> n;
  for (long i = 0; i < 4; i++) {
    for (long j = 0; j < n; j++) {
      for (long h = 0; h < n; h++) {
        cin >> mat[i][j][h];
      }
    }
  }
  for (long i = 0; i < 4; i++) {
    for (long j = 0; j < 4; j++) {
      for (long h = 0; h < 4; h++) {
        for (long g = 0; g < 4; g++) {
          if (i != j && i != h && i != g && j != h && j != g && h != g) {
            long long sol = 0;
            for (long t = 0; t < n; t++) {
              for (long r = 0; r < n; r++) {
                if (t % 2 == 0) {
                  if (r % 2 == 0) {
                    if (mat[i][t][r] != '1') {
                      sol++;
                    }
                    if (mat[j][t][r] != '1') {
                      sol++;
                    }
                  } else {
                    if (mat[i][t][r] != '0') {
                      sol++;
                    }
                    if (mat[j][t][r] != '0') {
                      sol++;
                    }
                  }
                } else {
                  if (r % 2 == 0) {
                    if (mat[i][t][r] != '0') {
                      sol++;
                    }
                    if (mat[j][t][r] != '0') {
                      sol++;
                    }
                  } else {
                    if (mat[i][t][r] != '1') {
                      sol++;
                    }
                    if (mat[j][t][r] != '1') {
                      sol++;
                    }
                  }
                }
              }
            }
            for (long t = 0; t < n; t++) {
              for (long r = 0; r < n; r++) {
                if (t % 2 == 0) {
                  if (r % 2 == 0) {
                    if (mat[h][t][r] != '0') {
                      sol++;
                    }
                    if (mat[g][t][r] != '0') {
                      sol++;
                    }
                  } else {
                    if (mat[h][t][r] != '1') {
                      sol++;
                    }
                    if (mat[g][t][r] != '1') {
                      sol++;
                    }
                  }
                } else {
                  if (r % 2 == 0) {
                    if (mat[h][t][r] != '1') {
                      sol++;
                    }
                    if (mat[g][t][r] != '1') {
                      sol++;
                    }
                  } else {
                    if (mat[h][t][r] != '0') {
                      sol++;
                    }
                    if (mat[g][t][r] != '0') {
                      sol++;
                    }
                  }
                }
              }
            }
            minsol = min(minsol, sol);
          }
        }
      }
    }
  }
  cout << minsol << endl;
}
