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;
const int MAXN = 205;
char A[MAXN + 5][MAXN + 5];
int B[MAXN + 5][MAXN + 5];
char s[5][MAXN + 5][MAXN + 5];
int n;
void Init() {
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int a = 1; a <= n; a++)
      for (int b = 1; b <= n; b++) cin >> s[i][a][b];
  }
}
void Change(int t) {
  for (int i = 1; i <= 2 * n; i++) {
    int a = 0;
    if (i & 1)
      a = t;
    else
      a = 1 ^ t;
    for (int j = 1; j <= 2 * n; j++) {
      if (j & 1)
        B[i][j] = a;
      else
        B[i][j] = 1 ^ a;
    }
  }
}
bool Check(int a, int b, int c, int d) {
  int vis[5];
  memset(vis, 0, sizeof(vis));
  vis[a]++, vis[b]++, vis[c]++, vis[d]++;
  bool check = true;
  for (int i = 1; i <= 4; i++)
    if (!vis[i]) check = false;
  return check;
}
void Add(int a, int b, int c, int d) {
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) {
      A[i][j] = s[a][i][j];
      A[i][j + n] = s[b][i][j];
      A[i + n][j] = s[c][i][j];
      A[i + n][j + n] = s[d][i][j];
    }
}
void solve() {
  int Max = MAXN * MAXN;
  for (int t = 0; t <= 1; t++) {
    Change(t);
    for (int a = 1; a <= 4; a++)
      for (int b = 1; b <= 4; b++)
        for (int c = 1; c <= 4; c++)
          for (int d = 1; d <= 4; d++) {
            if (Check(a, b, c, d)) {
              Add(a, b, c, d);
              int sum = 0;
              for (int i = 1; i <= 2 * n; i++)
                for (int j = 1; j <= 2 * n; j++)
                  if (A[i][j] != B[i][j] + '0') sum++;
              Max = min(Max, sum);
            }
          }
  }
  cout << Max << endl;
}
int main() {
  Init();
  solve();
}
