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;
long long n;
long long mat0[200][200];
long long mat1[200][200];
long long mat2[200][200];
long long mat3[200][200];
long long matrix[400][400];
long long type1[400][400];
long long type2[400][400];
void fill(long long a[][200], long long b[][200], long long c[][200],
          long long d[][200]) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      matrix[i][j] = a[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      matrix[i][j + n] = b[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      matrix[i + n][j] = c[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      matrix[i + n][j + n] = d[i][j];
    }
  }
}
long long find_ans() {
  long long cnt = 0;
  long long minn = 1e18;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (type1[i][j] != matrix[i][j]) {
        cnt++;
      }
    }
  }
  minn = min(minn, cnt);
  cnt = 0;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (type2[i][j] != matrix[i][j]) {
        cnt++;
      }
    }
  }
  minn = min(minn, cnt);
  return minn;
}
int main() {
  cin >> n;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      type1[i][j] = (i + j) % 2;
      type2[i][j] = 1 - type1[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char c;
      cin >> c;
      mat0[i][j] = c - '0';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char c;
      cin >> c;
      mat1[i][j] = c - '0';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char c;
      cin >> c;
      mat2[i][j] = c - '0';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char c;
      cin >> c;
      mat3[i][j] = c - '0';
    }
  }
  long long ans = 1e18;
  fill(mat0, mat1, mat2, mat3);
  ans = min(ans, find_ans());
  fill(mat0, mat1, mat3, mat2);
  ans = min(ans, find_ans());
  fill(mat0, mat2, mat3, mat1);
  ans = min(ans, find_ans());
  fill(mat0, mat2, mat1, mat3);
  ans = min(ans, find_ans());
  fill(mat0, mat3, mat1, mat2);
  ans = min(ans, find_ans());
  fill(mat0, mat3, mat2, mat1);
  ans = min(ans, find_ans());
  cout << ans << "\n";
  return 0;
}
