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>
void dfs(const int counts[4][2], std::vector<bool> &used,
         std::vector<int> &stack, int &min) {
  if (stack.size() == 4) {
    int count = counts[stack[0]][0] + counts[stack[1]][1] +
                counts[stack[2]][1] + counts[stack[3]][0];
    min = std::min(min, count);
    return;
  }
  for (int i = 0; i < used.size(); i++) {
    if (!used[i]) {
      used[i] = true;
      stack.emplace_back(i);
      dfs(counts, used, stack, min);
      used[i] = false;
      stack.pop_back();
    }
  }
}
int main(void) {
  int n;
  std::cin >> n;
  std::vector<std::vector<std::string>> boards(4, std::vector<std::string>(n));
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) {
      std::cin >> boards[k][i];
    }
  }
  int counts[4][2] = {0};
  for (int k = 0; k < 4; k++) {
    int changed = 0, changed2 = 0;
    char target = '1', target2 = '0';
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (boards[k][i][j] != target) {
          changed++;
        }
        if (boards[k][i][j] != target2) {
          changed2++;
        }
        target = '1' - target + '0';
        target2 = '1' - target2 + '0';
      }
    }
    counts[k][0] = changed;
    counts[k][1] = changed2;
  }
  int min = INT_MAX;
  std::vector<bool> used(4, false);
  std::vector<int> stack;
  dfs(counts, used, stack, min);
  std::cout << min << '\n';
  return 0;
}
