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, temp;
  int ar[4][2];
  string s;
  cin >> n;
  bool mat[4][109][109];
  for (int c = 0; c < 4; ++c) {
    for (int i = 0; i < n; ++i) {
      cin >> s;
      for (int j = 0; j < n; ++j) {
        s[j] == '0' ? mat[c][i][j] = 0 : mat[c][i][j] = 1;
      }
    }
  }
  bool co[4][109][109];
  for (int c = 0; c < 4; c++) {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        co[c][i][j] = mat[c][i][j];
      }
    }
  }
  for (int c = 0; c < 4; c++) {
    for (int b = 0; b < 2; ++b) {
      int cnt = 0;
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          if (b) {
            if (j == 0 && i % 2 == 0 && !co[c][i][j]) {
              co[c][i][j] = 1;
              cnt++;
            }
            if (j == 0 && i % 2 != 0 && co[c][i][j]) {
              co[c][i][j] = 0;
              cnt++;
            }
            if (j < n - 1) {
              if (co[c][i][j] == co[c][i][j + 1]) {
                co[c][i][j + 1] = !co[c][i][j + 1];
                cnt++;
              }
            }
          } else {
            if (j == 0 && i % 2 == 0 && co[c][i][j]) {
              co[c][i][j] = 0;
              cnt++;
            }
            if (j == 0 && i % 2 != 0 && !co[c][i][j]) {
              co[c][i][j] = 1;
              cnt++;
            }
            if (j < n - 1) {
              if (co[c][i][j] == co[c][i][j + 1]) {
                co[c][i][j + 1] = !co[c][i][j + 1];
                cnt++;
              }
            }
          }
        }
      }
      ar[c][b] = cnt;
      for (int c = 0; c < 4; c++) {
        for (int i = 0; i < n; ++i) {
          for (int j = 0; j < n; ++j) {
            co[c][i][j] = mat[c][i][j];
          }
        }
      }
    }
  }
  int Fucking_ans = 1e9;
  for (int i = 0; i < 4; ++i) {
    for (int j = i + 1; j < 4; ++j) {
      int cnt = 0;
      cnt += ar[i][0];
      cnt += ar[j][0];
      for (int k = 0; k < 4; ++k) {
        if (k == i || k == j) continue;
        cnt += ar[k][1];
      }
      Fucking_ans = min(Fucking_ans, cnt);
    }
  }
  cout << Fucking_ans;
  return 0;
}
