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 main() {
  int n;
  cin >> n;
  int type1[n][n], type2[n][n], s;
  for (int i = 0; i < n; i++) {
    if (i % 2 == 0)
      s = 1;
    else
      s = 0;
    for (int j = 0; j < n; j++) type1[i][j] = s, s = 1 - s;
  }
  for (int i = 0; i < n; i++) {
    if (i % 2 == 1)
      s = 1;
    else
      s = 0;
    for (int j = 0; j < n; j++) type2[i][j] = s, s = 1 - s;
  }
  string str;
  int mat[n][n], cost[4][2];
  memset(cost, 0, sizeof(cost));
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      cin >> str;
      assert(str.length() == n);
      for (int k = 0; k < n; k++) mat[j][k] = str[k] - '0';
    }
    for (int row = 0; row < n; row++)
      for (int col = 0; col < n; col++)
        if (mat[row][col] != type1[row][col]) cost[i][0] += 1;
    for (int row = 0; row < n; row++)
      for (int col = 0; col < n; col++)
        if (mat[row][col] != type2[row][col]) cost[i][1] += 1;
  }
  int ans = INT_MAX;
  ans = min(ans, cost[0][0] + cost[1][0] + cost[2][1] + cost[3][1]);
  ans = min(ans, cost[0][0] + cost[2][0] + cost[1][1] + cost[3][1]);
  ans = min(ans, cost[0][0] + cost[3][0] + cost[1][1] + cost[2][1]);
  ans = min(ans, cost[1][0] + cost[2][0] + cost[0][1] + cost[3][1]);
  ans = min(ans, cost[1][0] + cost[3][0] + cost[0][1] + cost[2][1]);
  ans = min(ans, cost[2][0] + cost[3][0] + cost[0][1] + cost[1][1]);
  cout << ans << endl;
}
