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>
const int INF = 0x3f3f3f3f;
using namespace std;
char mp1[105][105];
char mp2[105][105];
char G1[105][105];
char G2[105][105];
char G3[105][105];
char G4[105][105];
int G_4[4][2];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    if (i % 2)
      mp1[i][0] = '1';
    else
      mp1[i][0] = '0';
    for (int j = 1; j < n; j++) {
      if (mp1[i][j - 1] == '0')
        mp1[i][j] = '1';
      else
        mp1[i][j] = '0';
    }
  }
  for (int i = 0; i < n; i++) {
    if (i % 2)
      mp2[i][0] = '0';
    else
      mp2[i][0] = '1';
    for (int j = 1; j < n; j++) {
      if (mp2[i][j - 1] == '0')
        mp2[i][j] = '1';
      else
        mp2[i][j] = '0';
    }
  }
  for (int i = 0; i < n; i++) scanf("%s", G1[i]);
  for (int i = 0; i < n; i++) scanf("%s", G2[i]);
  for (int i = 0; i < n; i++) scanf("%s", G3[i]);
  for (int i = 0; i < n; i++) scanf("%s", G4[i]);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (G1[i][j] != mp1[i][j]) G_4[0][0]++;
      if (G1[i][j] != mp2[i][j]) G_4[0][1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (G2[i][j] != mp1[i][j]) G_4[1][0]++;
      if (G2[i][j] != mp2[i][j]) G_4[1][1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (G3[i][j] != mp1[i][j]) G_4[2][0]++;
      if (G3[i][j] != mp2[i][j]) G_4[2][1]++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (G4[i][j] != mp1[i][j]) G_4[3][0]++;
      if (G4[i][j] != mp2[i][j]) G_4[3][1]++;
    }
  }
  int ans = INF;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (i == j) continue;
      for (int k = 0; k < 4; k++) {
        if (k == i || k == j) continue;
        int temp = 6 - i - j - k, temp_sum = 0;
        temp_sum += G_4[i][0] + G_4[j][0];
        temp_sum += G_4[k][1] + G_4[temp][1];
        ans = min(ans, temp_sum);
      }
    }
  }
  printf("%d\n", ans);
}
