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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long minm = 1e9 + 7;
  int n;
  cin >> n;
  int v1[n][n], v2[n][n], v3[n][n], v4[n][n], v5[n][n];
  std::vector<int> v(4);
  int count1 = 0, count2 = 0, count3 = 0, count4 = 0;
  char c1[n][n], c2[n][n], c3[n][n], c4[n][n];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0)
        v5[i][j] = 1;
      else
        v5[i][j] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> c1[i][j];
      v1[i][j] = int(c1[i][j]) - int('0');
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> c2[i][j];
      v2[i][j] = int(c2[i][j]) - int('0');
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> c3[i][j];
      v3[i][j] = int(c3[i][j]) - int('0');
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> c4[i][j];
      v4[i][j] = int(c4[i][j]) - int('0');
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (v1[i][j] != v5[i][j]) count1++;
      if (v2[i][j] != v5[i][j]) count2++;
      if (v3[i][j] != v5[i][j]) count3++;
      if (v4[i][j] != v5[i][j]) count4++;
    }
  }
  v[0] = count1;
  v[1] = count2;
  v[2] = count3;
  v[3] = count4;
  sort(v.begin(), v.end());
  cout << v[0] + v[1] + 2 * n * n - (v[3] + v[2]);
  return 0;
}
