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;
int main() {
  int n;
  cin >> n;
  vector<string> A(n), B(n), C(n), D(n);
  vector<string> X(2 * n);
  for (int i = 0; i < n; i++) {
    cin >> A[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> B[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> C[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> D[i];
  }
  vector<int> count(12, 0);
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += B[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = C[i - n];
    X[i] += D[i - n];
  }
  char seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[0]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[0]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[1]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += B[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = D[i - n];
    X[i] += C[i - n];
  }
  seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[2]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[2]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[3]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[3]++;
    }
  }
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += C[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = B[i - n];
    X[i] += D[i - n];
  }
  seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[4]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[4]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[5]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[5]++;
    }
  }
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += C[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = D[i - n];
    X[i] += B[i - n];
  }
  seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[6]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[6]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[7]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[7]++;
    }
  }
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += D[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = C[i - n];
    X[i] += B[i - n];
  }
  seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[8]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[8]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[9]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[9]++;
    }
  }
  for (int i = 0; i < n; i++) {
    X[i] = A[i];
    X[i] += D[i];
  }
  for (int i = n; i < 2 * n; i++) {
    X[i] = B[i - n];
    X[i] += C[i - n];
  }
  seed = '0';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[10]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[10]++;
    }
  }
  seed = '1';
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0 && X[i][j] != seed) count[11]++;
      if ((i + j) % 2 == 1 && X[i][j] == seed) count[11]++;
    }
  }
  sort(count.begin(), count.end());
  cout << count[0] << endl;
  return 0;
}
