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 bool SUBMIT = 1;
int n, cnt, mincnt = (int)(1e9);
char one[102][102], zero[102][102];
int variations[4];
string chess[4][102];
int main() {
  if (SUBMIT) {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
  } else
    freopen("i.txt", "r", stdin);
  cin >> n;
  for (int k = 0; k < 4; ++k) {
    for (int i = 0; i < n; ++i) {
      cin >> chess[k][i];
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + 1) & 1) {
        if ((j + 1) & 1)
          one[i][j] = '1';
        else
          one[i][j] = '0';
      } else {
        if ((j + 1) & 1)
          one[i][j] = '0';
        else
          one[i][j] = '1';
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + 1) & 1) {
        if ((j + 1) & 1)
          zero[i][j] = '0';
        else
          zero[i][j] = '1';
      } else {
        if ((j + 1) & 1)
          zero[i][j] = '1';
        else
          zero[i][j] = '0';
      }
    }
  }
  for (int i = 0; i < 4; ++i) variations[i] = i;
  do {
    cnt = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (chess[variations[0]][i][j] != one[i][j]) cnt++;
        if (chess[variations[3]][i][j] != one[i][j]) cnt++;
        if (chess[variations[1]][i][j] != zero[i][j]) cnt++;
        if (chess[variations[2]][i][j] != zero[i][j]) cnt++;
      }
    }
    mincnt = min(mincnt, cnt);
    cnt = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (chess[variations[1]][i][j] != one[i][j]) cnt++;
        if (chess[variations[2]][i][j] != one[i][j]) cnt++;
        if (chess[variations[0]][i][j] != zero[i][j]) cnt++;
        if (chess[variations[3]][i][j] != zero[i][j]) cnt++;
      }
    }
    mincnt = min(mincnt, cnt);
  } while (next_permutation(variations, variations + 4));
  cout << mincnt << '\n';
  return 0;
}
