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() {
  long long n, k, m, i, j, ma = 0, sum = 0;
  cin >> n;
  long long p1[n][n], p2[n][n], p3[n][n], p4[n][n];
  long long t1[n][n], t2[n][n];
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((i % 2 == 0 && j % 2 == 0) || (i % 2 == 1 && j % 2 == 1)) {
        t1[i][j] = 1;
        t2[i][j] = 0;
      } else {
        t1[i][j] = 0;
        t2[i][j] = 1;
      }
    }
  }
  long long t = 4;
  string s;
  while (t--) {
    for (i = 0; i < n; i++) {
      cin >> s;
      if (t == 3) {
        for (j = 0; j < n; j++) {
          if (s[j] == '1')
            p4[i][j] = 1;
          else
            p4[i][j] = 0;
        }
      } else if (t == 2) {
        for (j = 0; j < n; j++) {
          if (s[j] == '1')
            p3[i][j] = 1;
          else
            p3[i][j] = 0;
        }
      } else if (t == 1) {
        for (j = 0; j < n; j++) {
          if (s[j] == '1')
            p2[i][j] = 1;
          else
            p2[i][j] = 0;
        }
      } else {
        for (j = 0; j < n; j++) {
          if (s[j] == '1')
            p1[i][j] = 1;
          else
            p1[i][j] = 0;
        }
      }
    }
  }
  long long ct1[5], ct2[5], mit1 = 10e10, mit2 = 10e10;
  for (i = 0; i < 6; i++) {
    ct1[i] = 0;
    ct2[i] = 0;
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t1[i][j] != p1[i][j]) ct1[1]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t2[i][j] != p1[i][j]) ct2[1]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t1[i][j] != p2[i][j]) ct1[2]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t2[i][j] != p2[i][j]) ct2[2]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t1[i][j] != p3[i][j]) ct1[3]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t2[i][j] != p3[i][j]) ct2[3]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t1[i][j] != p4[i][j]) ct1[4]++;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (t2[i][j] != p4[i][j]) ct2[4]++;
    }
  }
  long long mi = 10e10;
  mi = min(ct1[1] + ct1[2] + ct2[3] + ct2[4], mi);
  mi = min(ct1[1] + ct1[3] + ct2[2] + ct2[4], mi);
  mi = min(ct1[1] + ct1[4] + ct2[2] + ct2[3], mi);
  mi = min(ct1[2] + ct1[3] + ct2[1] + ct2[4], mi);
  mi = min(ct1[2] + ct1[4] + ct2[1] + ct2[3], mi);
  mi = min(ct1[3] + ct1[4] + ct2[1] + ct2[2], mi);
  cout << mi;
  return 0;
}
