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 a, b, c, d, a1, b1, c1, d1;
int main() {
  long long n;
  cin >> n;
  string s[n];
  for (int i = 0; i < n; i++) cin >> s[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          if (s[i][j] == '0')
            a++;
          else
            a1++;
        }
        if (j % 2 == 1) {
          if (s[i][j] == '1')
            a++;
          else
            a1++;
        }
      } else {
        if (j % 2 == 0) {
          if (s[i][j] == '1')
            a++;
          else
            a1++;
        }
        if (j % 2 == 1) {
          if (s[i][j] == '0')
            a++;
          else
            a1++;
        }
      }
    }
  }
  string s2[n];
  for (int i = 0; i < n; i++) cin >> s2[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          if (s2[i][j] == '0')
            b++;
          else
            b1++;
        }
        if (j % 2 == 1) {
          if (s2[i][j] == '1')
            b++;
          else
            b1++;
        }
      } else {
        if (j % 2 == 0) {
          if (s2[i][j] == '1')
            b++;
          else
            b1++;
        }
        if (j % 2 == 1) {
          if (s2[i][j] == '0')
            b++;
          else
            b1++;
        }
      }
    }
  }
  string s3[n];
  for (int i = 0; i < n; i++) cin >> s3[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          if (s3[i][j] == '0')
            c++;
          else
            c1++;
        }
        if (j % 2 == 1) {
          if (s3[i][j] == '1')
            c++;
          else
            c1++;
        }
      } else {
        if (j % 2 == 0) {
          if (s3[i][j] == '1')
            c++;
          else
            c1++;
        }
        if (j % 2 == 1) {
          if (s3[i][j] == '0')
            c++;
          else
            c1++;
        }
      }
    }
  }
  string s4[n];
  for (int i = 0; i < n; i++) cin >> s4[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          if (s4[i][j] == '0')
            d++;
          else
            d1++;
        }
        if (j % 2 == 1) {
          if (s4[i][j] == '1')
            d++;
          else
            d1++;
        }
      } else {
        if (j % 2 == 0) {
          if (s4[i][j] == '1')
            d++;
          else
            d1++;
        }
        if (j % 2 == 1) {
          if (s4[i][j] == '0')
            d++;
          else
            d1++;
        }
      }
    }
  }
  long long m = INT_MAX;
  m = min(a + b + c1 + d1, m);
  m = min(a + b1 + c + d1, m);
  m = min(a + b1 + c1 + d, m);
  m = min(a1 + b + c + d1, m);
  m = min(a1 + b + c1 + d, m);
  m = min(a1 + b1 + c + d, m);
  cout << m;
}
