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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  char mat1[n + 2][n + 2];
  char mat2[n + 2][n + 2];
  char mat3[n + 2][n + 2];
  char mat4[n + 2][n + 2];
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> mat1[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> mat2[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> mat3[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> mat4[i][j];
    }
  }
  char zero[n + 2][n + 2];
  char one[n + 2][n + 2];
  char x = '0';
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (x == '0')
        zero[i][j] = '0';
      else
        zero[i][j] = '1';
      if (x == '0')
        one[i][j] = '1';
      else
        one[i][j] = '0';
      if (x == '0')
        x = '1';
      else
        x = '0';
    }
  }
  int cost[6][3] = {0};
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (mat1[i][j] != one[i][j]) {
        cost[1][1]++;
      } else {
        cost[1][0]++;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (mat2[i][j] != one[i][j]) {
        cost[2][1]++;
      } else {
        cost[2][0]++;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (mat3[i][j] != one[i][j]) {
        cost[3][1]++;
      } else {
        cost[3][0]++;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (mat4[i][j] != one[i][j]) {
        cost[4][1]++;
      } else {
        cost[4][0]++;
      }
    }
  }
  int ans = 100000008;
  ans = min(ans, cost[1][0] + cost[2][1] + cost[3][0] + cost[4][1]);
  ans = min(ans, cost[1][0] + cost[2][0] + cost[3][1] + cost[4][1]);
  ans = min(ans, cost[1][0] + cost[2][1] + cost[3][1] + cost[4][0]);
  ans = min(ans, cost[1][1] + cost[2][1] + cost[3][0] + cost[4][0]);
  ans = min(ans, cost[1][1] + cost[2][0] + cost[3][0] + cost[4][1]);
  ans = min(ans, cost[1][1] + cost[2][0] + cost[3][1] + cost[4][0]);
  cout << ans << "\n";
  return 0;
}
