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>
const int mod = 1000000007;
using namespace std;
int main() {
  int n;
  cin >> n;
  char ch;
  int a[4], b[4];
  for (int i = 0; i < 4; i++) {
    a[i] = 0;
    b[i] = 0;
  }
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        cin >> ch;
        if ((k + j) % 2 == 0 && ch == '1') a[i]++;
        if ((k + j) % 2 == 1 && ch == '0') a[i]++;
        if ((k + j) % 2 == 0 && ch == '0') b[i]++;
        if ((k + j) % 2 == 1 && ch == '1') b[i]++;
      }
    }
  }
  int ans = INT_MAX;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (j == i) continue;
      int sum = a[i] + a[j];
      bool bb[4];
      for (int i = 0; i < 4; i++) bb[i] = 0;
      bb[i] = 1;
      bb[j] = 1;
      for (int m = 0; m < 4; m++)
        if (!bb[m]) sum += b[m];
      ans = min(ans, sum);
    }
  }
  cout << ans;
  return 0;
}
