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 N;
int black[4][101][101];
int settl(int t, int c) {
  int ans = 0;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N; ++j) {
      if ((i + j) % 2 == 0) {
        if (black[t][i][j] != c) ++ans;
      } else {
        if (black[t][i][j] == c) ++ans;
      }
    }
  }
  return ans;
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin >> N;
  for (int i = 0; i < 4; ++i) {
    for (int n = 0; n < N; ++n) {
      for (int n2 = 0; n2 < N; ++n2) {
        char inp;
        cin >> inp;
        black[i][n][n2] = inp == '1';
      }
    }
  }
  vector<int> p = vector<int>(4);
  for (int i = 0; i < 4; ++i) p[i] = i;
  int best = 1 << 25;
  while (next_permutation(p.begin(), p.end())) {
    int ans = settl(p[0], 1) + settl(p[1], 0) + settl(p[2], 0) + settl(p[3], 1);
    int ans2 =
        settl(p[0], 0) + settl(p[1], 1) + settl(p[2], 1) + settl(p[3], 0);
    int mn = ans > ans2 ? ans2 : ans;
    best = best > mn ? mn : best;
  }
  cout << best;
}
