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;
string a[120];
string b[120];
string c[120];
string d[120];
int calc0(string s[120], int n) {
  int cnt = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + j) % 2 == 0) {
        if (s[i][j] != '1') cnt++;
      } else {
        if (s[i][j] != '0') cnt++;
      }
    }
  }
  return cnt;
}
int calc1(string s[120], int n) {
  int cnt = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + j) % 2 == 0) {
        if (s[i][j] != '0') cnt++;
      } else {
        if (s[i][j] != '1') cnt++;
      }
    }
  }
  return cnt;
}
int main() {
  int n;
  while (cin >> n) {
    for (int i = 0; i < n; ++i) cin >> a[i];
    int numa0 = calc0(a, n);
    int numa1 = calc1(a, n);
    for (int i = 0; i < n; ++i) cin >> b[i];
    int numb0 = calc0(b, n);
    int numb1 = calc1(b, n);
    for (int i = 0; i < n; ++i) cin >> c[i];
    int numc0 = calc0(c, n);
    int numc1 = calc1(c, n);
    for (int i = 0; i < n; ++i) cin >> d[i];
    int numd0 = calc0(d, n);
    int numd1 = calc1(d, n);
    int sum =
        min({numa0 + numb0 + numc1 + numd1, numa0 + numb1 + numc1 + numd0,
             numa1 + numb1 + numc0 + numd0, numa1 + numb0 + numc0 + numd1,
             numa1 + numb0 + numc1 + numd0, numa0 + numb1 + numc0 + numd1});
    cout << sum << endl;
  }
  return 0;
}
