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;
using ll = long long;
using ii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
int n;
int diff(const vvi &a, const vvi &b) {
  int ans = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      ans += a[i][j] != b[i][j];
    }
  }
  return ans;
}
void print(const vvi &a) {
  for (auto i : a) {
    for (auto j : i) {
      cout << j << " ";
    }
    cout << endl;
  }
  cout << endl;
}
int main() {
  scanf("%d\n", &n);
  vvi white(n, vi(n)), black(n, vi(n));
  bool c = false;
  for (auto &i : white) {
    for (int &j : i) {
      j = c;
      c = !c;
    }
  }
  c = true;
  for (auto &i : black) {
    for (int &j : i) {
      j = c;
      c = !c;
    }
  }
  vector<vvi> b(4, vvi(n, vi(n)));
  for (int k = 0; k < 4; ++k) {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        scanf("%1d", &b[k][i][j]);
      }
    }
    getchar();
  }
  int ans = 1234567890;
  int mask = 0;
  while (mask != 16) {
    if (__builtin_popcount(mask) != 2) {
      ++mask;
      continue;
    }
    int res = 0;
    for (int bit = 0; bit < 4; ++bit) {
      if ((1 << bit) & mask) {
        res += diff(black, b[bit]);
      } else {
        res += diff(white, b[bit]);
      }
    }
    ans = min(ans, res);
    ++mask;
  }
  printf("%d\n", ans);
  return 0;
}
