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;
char a[5][108][108];
vector<int> p;
int c[208][208];
int res = 1e9;
int n;
void calc() {
  for (int x = 0; x < 4; x++) {
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        if (p[x] == 1) {
          c[i][j] = a[x + 1][i][j];
        } else if (p[x] == 2) {
          c[i][j + n] = a[x + 1][i][j];
        } else if (p[x] == 3) {
          c[i + n][j] = a[x + 1][i][j];
        } else if (p[x] == 4) {
          c[i + n][j + n] = a[x + 1][i][j];
        }
      }
    }
  }
  int cnt = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      cnt += ((i + j) % 2 != c[i][j] % 2);
    }
  }
  res = min(res, cnt);
  cnt = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      cnt += ((i + j + 1) % 2 != c[i][j] % 2);
    }
  }
  res = min(res, cnt);
}
int main() {
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) cin >> a[i][j] + 1;
  }
  for (int i = 1; i <= 4; i++) p.push_back(i);
  do {
    calc();
  } while (next_permutation(p.begin(), p.end()));
  cout << res;
}
