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;
const int maxn = 1e6 + 2;
long long int count(string str[], long long int n) {
  long long int i, j, ans = 0, c1 = 0, c2 = 0;
  for (i = 0; i < 2 * n; ++i) {
    for (j = 0; j < 2 * n; ++j) {
      if ((i + j) % 2 == 0 && (str[i][j] == '1')) ++c1;
      if ((i + j) % 2 == 1 && (str[i][j] == '0')) ++c1;
    }
  }
  for (i = 0; i < 2 * n; ++i) {
    for (j = 0; j < 2 * n; ++j) {
      if ((i + j) % 2 == 0 && str[i][j] == '0') c2++;
      if ((i + j) % 2 == 1 && str[i][j] == '1') ++c2;
    }
  }
  ans = min(c1, c2);
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int i, j, k, l, m, n, anss = LONG_LONG_MAX, one = 0, zero = 0;
  cin >> n;
  string str[5][300];
  for (i = 1; i <= 4; ++i) {
    for (j = 0; j < n; ++j) cin >> str[i][j];
  }
  for (i = 1; i <= 4; ++i) {
    for (j = 1; j <= 4; ++j) {
      for (k = 1; k <= 4; ++k) {
        for (l = 1; l <= 4; ++l) {
          if (i != j && i != k && i != l && j != k && j != l & k != l) {
            string ans[509];
            for (m = 0; m < n; ++m) ans[m] += str[i][m];
            for (m = 0; m < n; ++m) ans[m] += str[j][m];
            for (m = n; m < 2 * n; ++m) ans[m] += str[k][m - n];
            for (m = n; m < 2 * n; ++m) ans[m] += str[l][m - n];
            anss = min(count(ans, n), anss);
          }
        }
      }
    }
  }
  cout << anss;
}
