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;
string grid[101];
string p[4][101];
int n;
int co(int arr[]) {
  for (int i = 0; i < n; i++) grid[i] = p[arr[0]][i];
  for (int i = 0; i < n; i++) grid[i] += p[arr[1]][i];
  for (int i = 0; i < n; i++) grid[i + n] = p[arr[2]][i];
  for (int i = 0; i < n; i++) grid[i + n] += p[arr[3]][i];
  int co = 0;
  if (grid[0][0] != '0') grid[0][0] = '0', co++;
  for (int i = 0; i < 2 * n; i++) {
    if (i != 0 && grid[i][0] == grid[i - 1][0])
      co++, grid[i][0] = grid[i][0] == '1' ? '0' : '1';
    for (int j = 1; j < 2 * n; j++)
      if (grid[i][j] == grid[i][j - 1])
        co++, grid[i][j] = grid[i][j] == '1' ? '0' : '1';
  }
  int co2 = 0;
  for (int i = 0; i < n; i++) grid[i] = p[arr[0]][i];
  for (int i = 0; i < n; i++) grid[i] += p[arr[1]][i];
  for (int i = 0; i < n; i++) grid[i + n] = p[arr[2]][i];
  for (int i = 0; i < n; i++) grid[i + n] += p[arr[3]][i];
  if (grid[0][0] != '1') grid[0][0] = '1', co2++;
  for (int i = 0; i < 2 * n; i++) {
    if (i != 0 && grid[i][0] == grid[i - 1][0])
      co2++, grid[i][0] = grid[i][0] == '1' ? '0' : '1';
    for (int j = 1; j < 2 * n; j++)
      if (grid[i][j] == grid[i][j - 1])
        co2++, grid[i][j] = grid[i][j] == '1' ? '0' : '1';
  }
  return min(co, co2);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) cin >> p[i][j];
  }
  int arr[] = {0, 1, 2, 3};
  int mi = INT_MAX;
  do {
    mi = min(mi, co(arr));
  } while (next_permutation(arr, arr + 4));
  cout << mi << endl;
  return 0;
}
