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 int PI = 3.141592653589793;
const int inf = 1000111222;
const int N = 100007;
string chess[500];
int first[100], change[100], ans, bit[200];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int j = 0; j < 4; j++) {
    for (int i = 0; i < n; i++) cin >> chess[i];
    first[j] += (chess[0][0] == '1');
    int flag = first[j];
    for (int a = 0; a < n; a++) {
      for (int b = 0; b < n; b++) {
        int just = chess[a][b] - '0';
        if (just != flag) {
          change[j]++;
        }
        flag ^= 1;
      }
    }
  }
  ans = inf;
  for (int i = 0; i < 15; i++) {
    int cnt = 0;
    for (int i = 0; i < 20; i++) {
      bit[i] = 0;
    }
    for (int t = 0; t < 5; t++) {
      if ((1 << t) & i) {
        cnt++;
        bit[t] = 1;
      }
    }
    if (cnt != 2) continue;
    int curr = 0;
    for (int t = 0; t < 4; t++) {
      if (bit[t] == first[t]) {
        curr += change[t];
      } else {
        int x = n * n - change[t];
        curr += x;
      }
    }
    ans = min(ans, curr);
  }
  cout << ans << "\n";
  return 0;
}
