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;
const int MAXN = 105;
int n;
char a[MAXN][MAXN][5];
vector<int> v;
char option1[2 * MAXN][2 * MAXN], option2[2 * MAXN][2 * MAXN];
int main() {
  int current, current1, answer = INT_MAX;
  cin >> n;
  for (int p = 0; p < 4; p++) {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) cin >> a[i][j][p];
    }
  }
  v.push_back(0);
  v.push_back(1);
  v.push_back(2);
  v.push_back(3);
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          option1[i][j] = '0';
          option2[i][j] = '1';
        } else {
          option1[i][j] = '1';
          option2[i][j] = '0';
        }
      } else {
        if (j % 2 == 0) {
          option1[i][j] = '1';
          option2[i][j] = '0';
        } else {
          option1[i][j] = '0';
          option2[i][j] = '1';
        }
      }
    }
  }
  do {
    current = 0;
    current1 = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (a[i][j][v[0]] != option1[i][j]) current++;
        if (a[i][j][v[0]] != option2[i][j]) current1++;
      }
    }
    for (int i = n; i < 2 * n; i++) {
      for (int j = 0; j < n; j++) {
        if (a[i - n][j][v[1]] != option1[i][j]) current++;
        if (a[i - n][j][v[1]] != option2[i][j]) current1++;
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = n; j < 2 * n; j++) {
        if (a[i][j - n][v[2]] != option1[i][j]) current++;
        if (a[i][j - n][v[2]] != option2[i][j]) current1++;
      }
    }
    for (int i = n; i < 2 * n; i++) {
      for (int j = n; j < 2 * n; j++) {
        if (a[i - n][j - n][v[3]] != option1[i][j]) current++;
        if (a[i - n][j - n][v[3]] != option2[i][j]) current1++;
      }
    }
    answer = min(answer, current);
    answer = min(answer, current1);
  } while (next_permutation(v.begin(), v.end()));
  cout << answer << '\n';
}
