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;
const int MAXN = 101;
char a[MAXN][MAXN][4];
int N;
vector<int> s;
int ok() {
  int changea = 0;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[0]] == '0');
      } else
        changea += (a[i][j][s[0]] == '1');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[2]] == '0');
      } else
        changea += (a[i][j][s[2]] == '1');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[1]] == '1');
      } else
        changea += (a[i][j][s[1]] == '0');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[3]] == '1');
      } else
        changea += (a[i][j][s[3]] == '0');
    }
  return changea;
}
int ok1() {
  int changea = 0;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[0]] == '1');
      } else
        changea += (a[i][j][s[0]] == '0');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[2]] == '1');
      } else
        changea += (a[i][j][s[2]] == '0');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[1]] == '0');
      } else
        changea += (a[i][j][s[1]] == '1');
    }
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) {
      if ((i & 1 && j & 1) || (!(i & 1) && !(j & 1))) {
        changea += (a[i][j][s[3]] == '0');
      } else
        changea += (a[i][j][s[3]] == '1');
    }
  return changea;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  s.push_back(0);
  s.push_back(1);
  s.push_back(2);
  s.push_back(3);
  cin >> N;
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) cin >> a[i][j][0];
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) cin >> a[i][j][1];
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) cin >> a[i][j][2];
  for (int i = 1; i <= N; i++)
    for (int j = 1; j <= N; j++) cin >> a[i][j][3];
  int sol = 4 * N * N;
  do {
    int k = ok();
    if (k < sol) sol = k;
    k = ok1();
    if (k < sol) sol = k;
  } while (next_permutation(s.begin(), s.end()));
  cout << sol;
  return 0;
}
