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 INF = 1e9;
vector<int> a = {0, 1, 2, 3};
vector<vector<string>> x;
vector<string> y;
int n, asd, ans = INF;
void build() {
  for (int i = 0; i < 2 * n; i++) y[i].clear();
  for (int i = 0; i < n; i++) {
    for (auto j : x[a[0]][i]) y[i].push_back(j);
    for (auto j : x[a[1]][i]) y[i].push_back(j);
  }
  for (int i = n; i < 2 * n; i++) {
    for (auto j : x[a[2]][i - n]) y[i].push_back(j);
    for (auto j : x[a[3]][i - n]) y[i].push_back(j);
  }
}
int f(char ul) {
  build();
  int res = 0;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) & 1) {
        if (y[i][j] == ul) res++;
      } else {
        if (y[i][j] != ul) res++;
      }
    }
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  x.resize(4);
  y.resize(2 * n);
  for (int i = 0; i < 4; i++) {
    x[i].resize(n);
    for (int j = 0; j < n; j++) cin >> x[i][j];
  }
  do {
    ans = min(ans, f('1'));
    ans = min(ans, f('0'));
  } while (next_permutation(a.begin(), a.end()));
  cout << ans << endl;
}
