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 const M = 1e5 + 10, N = 1e8 + 10, pi = acos(-1);
int n, a[4][111][111], b[222][222], x, ans = 1e9;
void dmj(int, int, int, int);
int f() {
  int ans = 0, k = b[0][0], mn;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (b[i][j] != k) ans++;
      if (j != 2 * n - 1) k = !k;
    }
  }
  mn = ans;
  ans = 1, k = b[0][0] = !b[0][0];
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (b[i][j] != k) ans++;
      if (j != 2 * n - 1) k = !k;
    }
  }
  return min(mn, ans);
}
void print() {
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      cout << b[i][j];
    }
    cout << endl;
  }
  cout << endl;
}
int main() {
  cin >> n;
  string s;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < n; j++) {
      cin >> s;
      for (int k = 0; k < n; k++) {
        a[i][j][k] = (s[k] == '1');
      }
    }
  for (int i1 = 0; i1 < 4; i1++)
    for (int i2 = 0; i2 < 4; i2++)
      if (i2 != i1)
        for (int i3 = 0; i3 < 4; i3++)
          if (i3 != i2 && i3 != i1)
            for (int i4 = 0; i4 < 4; i4++) {
              if (i4 != i3 && i4 != i2 && i4 != i1) {
                dmj(i1, i2, i3, i4);
                ans = min(ans, f());
              }
            }
  cout << ans;
}
void dmj(int i1, int i2, int i3, int i4) {
  int ii = 0, jj = 0, i, j;
  for (i = 0; i < n; i++, ii++) {
    for (j = 0, jj = 0; j < n; j++, jj++) {
      b[ii][jj] = a[i1][i][j];
    }
  }
  ii = 0;
  for (i = 0; i < n; i++, ii++) {
    for (j = 0, jj = n; j < n; j++, jj++) {
      b[ii][jj] = a[i2][i][j];
    }
  }
  jj = 0, ii = n;
  for (i = 0; i < n; i++, ii++) {
    for (j = 0, jj = 0; j < n; j++, jj++) {
      b[ii][jj] = a[i3][i][j];
    }
  }
  ii = jj = n;
  for (i = 0; i < n; i++, ii++) {
    for (j = 0, jj = n; j < n; j++, jj++) {
      b[ii][jj] = a[i4][i][j];
    }
  }
}
