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 int n, a[100][100], b[100][100], c[100][100], d[100][100];
long long int check(long long int x[][100], long long int y[][100],
                    long long int z[][100], long long int w[1][100]) {
  long long int count1 = 0;
  long long int i, j;
  for (i = 1; i <= 2 * n; i++)
    for (j = 1; j <= 2 * n; j++)
      if (j <= n) {
        if (i <= n) {
          if ((i + j) % 2 == 0) {
            if (x[i][j] == 1) count1++;
          } else {
            if (x[i][j] == 0) count1++;
          }
        } else {
          if ((i + j) % 2 == 0) {
            if (z[i - n][j] == 1) count1++;
          } else {
            if (z[i - n][j] == 0) count1++;
          }
        }
      } else {
        if (i <= n) {
          if ((i + j) % 2 == 0) {
            if (y[i][j - n] == 1) count1++;
          } else {
            if (y[i][j - n] == 0) count1++;
          }
        } else {
          if ((i + j) % 2 == 0) {
            if (w[i - n][j - n] == 1) count1++;
          } else {
            if (w[i - n][j - n] == 0) count1++;
          }
        }
      }
  long long int count2 = 0;
  for (i = 1; i <= 2 * n; i++)
    for (j = 1; j <= 2 * n; j++)
      if (j <= n) {
        if (i <= n) {
          if ((i + j) % 2 == 0) {
            if (x[i][j] == 0) count2++;
          } else {
            if (x[i][j] == 1) count2++;
          }
        } else {
          if ((i + j) % 2 == 0) {
            if (z[i - n][j] == 0) count2++;
          } else {
            if (z[i - n][j] == 1) count2++;
          }
        }
      } else {
        if (i <= n) {
          if ((i + j) % 2 == 0) {
            if (y[i][j - n] == 0) count2++;
          } else {
            if (y[i][j - n] == 1) count2++;
          }
        } else {
          if ((i + j) % 2 == 0) {
            if (w[i - n][j - n] == 0) count2++;
          } else {
            if (w[i - n][j - n] == 1) count2++;
          }
        }
      }
  return min(count1, count2);
}
int main() {
  long long int i, j;
  string s;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> s;
    for (j = 0; j < n; j++) a[i][j + 1] = (int)s[j] - 48;
  }
  for (i = 1; i <= n; i++) {
    cin >> s;
    for (j = 0; j < n; j++) b[i][j + 1] = (int)s[j] - 48;
  }
  for (i = 1; i <= n; i++) {
    cin >> s;
    for (j = 0; j < n; j++) c[i][j + 1] = (int)s[j] - 48;
  }
  for (i = 1; i <= n; i++) {
    cin >> s;
    for (j = 0; j < n; j++) d[i][j + 1] = (int)s[j] - 48;
  }
  long long int min1 = check(a, b, c, d);
  long long int min2 = check(a, b, d, c);
  long long int min3 = check(a, c, b, d);
  long long int min4 = check(a, c, d, b);
  long long int min5 = check(a, d, b, c);
  long long int min6 = check(a, d, c, b);
  cout << min(min(min(min(min(min1, min2), min3), min4), min5), min6);
}
