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;
int a[4][2];
int n;
int fun(string x, string y) {
  bitset<10000> bx(x);
  bitset<10000> by(y);
  bitset<10000> bz = bx ^ by;
  return bz.count();
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < 4; i++) {
    string str = "";
    for (int k = 0; k < n; k++) {
      string tmp;
      cin >> tmp;
      str += tmp;
    }
    string ori0;
    string ori1;
    int tmp = 0;
    for (int i = 0; i < n * n; i++) {
      ori0.push_back(tmp + '0');
      ori1.push_back((!tmp) + '0');
      tmp = !tmp;
    }
    a[i][0] = fun(str, ori0);
    a[i][1] = fun(str, ori1);
  }
  int x[6];
  x[0] = a[0][0] + a[1][0] + a[2][1] + a[3][1];
  x[1] = a[0][0] + a[1][1] + a[2][0] + a[3][1];
  x[2] = a[0][0] + a[1][1] + a[2][1] + a[3][0];
  x[3] = a[0][1] + a[1][0] + a[2][0] + a[3][1];
  x[4] = a[0][1] + a[1][0] + a[2][1] + a[3][0];
  x[5] = a[0][1] + a[1][1] + a[2][0] + a[3][0];
  sort(x, x + 6);
  cout << x[0] << endl;
}
