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 long long MX = 200, INF = 1e18, INF2 = -1e18, D = 1e9 + 7;
long long n;
long long mat[4][MX][MX];
long long mark[4][2];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (long long k = 0; k < 4; k++) {
    for (long long i = 0; i < n; i++) {
      string s;
      cin >> s;
      for (long long j = 0; j < n; j++) {
        mat[k][i][j] = int32_t(s[j] - '0');
      }
    }
  }
  for (long long k = 0; k < 4; k++) {
    for (long long l = 0; l < 2; l++) {
      for (long long i = 0; i < n; i++) {
        for (long long j = 0; j < n; j++) {
          if ((i + j) % 2 == 0) {
            if (mat[k][i][j] != l) mark[k][l]++;
          } else {
            if (mat[k][i][j] != (l ^ 1)) mark[k][l]++;
          }
        }
      }
    }
  }
  long long mn = INF;
  for (long long i = 0; i < 3; i++) {
    for (long long j = i + 1; j < 4; j++) {
      long long kl = mark[i][0] + mark[j][0];
      for (long long l = 0; l < 4; l++) {
        if (l != i && l != j) kl += mark[l][1];
      }
      mn = min(mn, kl);
    }
  }
  cout << mn;
  return 0;
}
