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 maxn = 100010;
char a[4][110][110];
int b[4][2];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n = 0, res = INT_MAX;
  cin >> n;
  for (int k = 0; k < 4; ++k)
    for (int i = 0; i < n; ++i) cin >> a[k][i];
  for (int k = 0; k < 4; ++k)
    for (int state = 0; state < 2; ++state) {
      int sum = 0;
      for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j) {
          int x = a[k][i][j] - '0';
          int y = (i + j + state) % 2;
          sum += abs(y - x);
        }
      b[k][state] = sum;
    }
  for (int i = 0; i < (1 << 4); ++i) {
    int ct = 0;
    for (int j = 0; j < 4; ++j) {
      if (i >> j & 1) ++ct;
    }
    if (ct != 2) continue;
    int temp = 0;
    for (int j = 0; j < 4; ++j) {
      if (i >> j & 1)
        temp += b[j][0];
      else
        temp += b[j][1];
    }
    res = min(res, temp);
  }
  cout << res;
}
