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 N = 110, M = 4, inF = N * N * N;
int n, ans = inF;
string s[M][N];
vector<int> vec = {0, 1, 2, 3};
int check(int dex, int b) {
  int res = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      res += (s[dex][i][j] - '0' != ((i + j + b) & 1));
  return res;
}
int get(vector<int> vec) {
  int res = 0;
  for (int i = 0; i < M; i++) res += check(vec[i], i & 1);
  return res;
}
int main() {
  cin >> n;
  for (int i = 0; i < M; i++)
    for (int j = 0; j < n; j++) cin >> s[i][j];
  do {
    ans = min(ans, get(vec));
  } while (next_permutation(vec.begin(), vec.end()));
  cout << ans;
  return 0;
}
