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>
std::vector<std::vector<int> > groups(4, std::vector<int>(2));
void make(std::vector<std::vector<int> > sk, int i, int n) {
  int bad = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i & 1) == (j & 1)) {
        if (sk[i][j] != 1) bad++;
      } else if (sk[i][j] == 1)
        bad++;
    }
  }
  groups[i][0] = bad;
  groups[i][1] = n * n - bad;
}
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int N;
  std::cin >> N;
  std::vector<std::vector<int> > sk(N, std::vector<int>(N));
  char ch;
  std::string str;
  for (int k = 0; k < 4; k++) {
    sk.clear();
    sk.resize(N, std::vector<int>(N));
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < N; j++) {
        std::cin >> ch;
        if (ch == '1') {
          sk[i][j] = 1;
        } else
          sk[i][j] = 0;
      }
    }
    make(sk, k, N);
  }
  int maz = 1000000000;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      for (int k = 0; k < 2; k++) {
        for (int l = 0; l < 2; l++) {
          if (i + j + k + l == 2) {
            maz = std::min(
                maz, groups[0][i] + groups[1][j] + groups[2][k] + groups[3][l]);
          }
        }
      }
    }
  }
  std::cout << maz << "\n";
  return 0;
}
