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;
template <class T>
using min_queue = priority_queue<T, vector<T>, greater<T>>;
template <typename Args>
void kill(Args args) {
  cout << args << "\n";
  exit(0);
}
const double PI = acos(-1);
const long long MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long LLINF = 0x3f3f3f3f3f3f3f3f;
int n;
int temp[5] = {0, 1, 2, 3, 4};
int arr[5][101][101];
void solve(int testnum) {
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      string s;
      cin >> s;
      for (int k = 1; k <= n; k++) {
        arr[i][j][k] = s[k - 1] - '0';
      }
    }
  }
  int minn = INF;
  do {
    int tmp[401][401];
    memset(tmp, -1, sizeof tmp);
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        tmp[i][j] = arr[temp[1]][i][j];
      }
    }
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        tmp[i][n + j] = arr[temp[2]][i][j];
      }
    }
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        tmp[i + n][j] = arr[temp[3]][i][j];
      }
    }
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        tmp[i + n][j + n] = arr[temp[4]][i][j];
      }
    }
    int res = 0;
    int col = tmp[1][1];
    for (int i = 1; i <= 2 * n; i++) {
      for (int j = 1; j <= 2 * n; j++) {
        if (tmp[i][j] != col) {
          res++;
        }
        if (j != 2 * n) col = !col;
      }
    }
    minn = min(minn, res);
    col = !tmp[1][1];
    res = 0;
    for (int i = 1; i <= 2 * n; i++) {
      for (int j = 1; j <= 2 * n; j++) {
        if (tmp[i][j] != col) {
          res++;
        }
        if (j != 2 * n) col = !col;
      }
    }
    minn = min(minn, res);
  } while (next_permutation(temp + 1, temp + 5));
  cout << minn << "\n";
}
void precompute() {}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout << fixed << setprecision(12);
  int testcase = 1;
  clock_t zzzx = clock();
  precompute();
  for (int i = 1; i <= testcase; i++) {
    solve(i);
  }
  double elapsed_time = (double)(clock() - zzzx) / CLOCKS_PER_SEC;
  cerr << "elapsed_time"
       << " = " << (elapsed_time) << "\n";
  return 0;
}
