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;
using ll = long long;
vector<size_t> ve[100103];
void pre() {
  int arr[100103];
  fill(arr, arr + 100103, 1);
  for (ll i = 2; i < 100103; i++) {
    if (arr[i]) {
      for (ll j = i; j < 100103; j += i) {
        arr[j] = 0;
        ve[j].push_back(i);
      }
    }
  }
}
int main() {
  int n;
  cin >> n;
  string str;
  int tt, x = 0, y = 0;
  vector<pair<int, int>> v;
  int s = 0;
  int bl[n][n];
  int wh[n][n];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2) {
        if (j % 2) {
          bl[i][j] = 1;
          wh[i][j] = 0;
        } else {
          bl[i][j] = 0;
          wh[i][j] = 1;
        }
      } else {
        if (j % 2) {
          bl[i][j] = 0;
          wh[i][j] = 1;
        } else {
          bl[i][j] = 1;
          wh[i][j] = 0;
        }
      }
    }
  }
  for (int i = 0; i < 4; i++) {
    x = 0;
    y = 0;
    for (int r = 0; r < n; r++) {
      cin >> str;
      for (int t = 0; t < n; t++) {
        tt = 0 * (str[t] == '0') + 1 * (str[t] == '1');
        if (tt != bl[r][t]) {
          x++;
        }
        if (tt != wh[r][t]) {
          y++;
        }
      }
    }
    v.push_back(make_pair(x, y));
  }
  int m = 100000000;
  for (int i = 0; i < 3; i++) {
    for (int j = i + 1; j <= 3; j++) {
      s = 0;
      for (int x = 0; x < 4; x++) {
        if (x != i && x != j) {
          s += v[x].first;
        }
      }
      s += v[i].second;
      s += v[j].second;
      if (s < m) {
        m = s;
      }
    }
  }
  cout << m << endl;
}
