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;
long long t, n, m;
long long chess[1111][1111];
long long a[10][111][111];
string s;
long long solve(int p, int q, int r, int s, int val) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      chess[i][j] = a[p][i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      chess[i + n][j] = a[q][i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      chess[i + n][j + n] = a[r][i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      chess[i][j + n] = a[s][i][j];
    }
  }
  long long ret = 0;
  if (chess[0][0] != val) {
    chess[0][0] = val;
    ret++;
  }
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (i == 0 && j == 0)
        continue;
      else if (j == 0) {
        if (chess[i][j] == chess[i - 1][j]) {
          ret++;
          chess[i][j] = !chess[i - 1][j];
        }
      } else {
        if (chess[i][j] == chess[i][j - 1]) {
          ret++;
          chess[i][j] = !chess[i][j - 1];
        }
      }
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char ch;
      cin >> ch;
      if (ch == '1')
        a[0][i][j] = 1;
      else
        a[0][i][j] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char ch;
      cin >> ch;
      if (ch == '1')
        a[1][i][j] = 1;
      else
        a[1][i][j] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char ch;
      cin >> ch;
      if (ch == '1')
        a[2][i][j] = 1;
      else
        a[2][i][j] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char ch;
      cin >> ch;
      if (ch == '1')
        a[3][i][j] = 1;
      else
        a[3][i][j] = 0;
    }
  }
  vector<int> perm;
  long long ans = LONG_LONG_MAX;
  perm.push_back(0);
  perm.push_back(1);
  perm.push_back(2);
  perm.push_back(3);
  do {
    ans = min(ans, solve(perm[0], perm[1], perm[2], perm[3], 1));
    ans = min(ans, solve(perm[0], perm[1], perm[2], perm[3], 0));
  } while (next_permutation(perm.begin(), perm.end()));
  cout << ans << "\n";
  return 0;
}
