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 N = 102, M = 1000000007, BIG = 0x3f3f3f3f;
int n;
int a[4][N][N];
int cost[2][4];
bool Read() {
  cin >> n;
  if (cin.eof()) return 0;
  char c;
  for (int k = 0; k < 4; k++)
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) {
        cin >> c;
        a[k][i][j] = c - '0';
      }
  return 1;
}
void Process() {
  memset(cost, 0, sizeof cost);
  for (int k = 0; k < 4; k++)
    for (int turn = 0; turn < 2; turn++) {
      bool cur = turn;
      for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++, cur = !cur)
          if (a[k][i][j] != cur) cost[turn][k]++;
    }
  int ans = BIG, cur = 0;
  for (int i = 0; i < 4; i++)
    for (int j = i + 1; j < 4; j++) {
      cur = cost[1][i] + cost[1][j];
      for (int k = 0; k < 4; k++)
        if (k != i && k != j) cur += cost[0][k];
      ans = min(ans, cur);
    }
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  while (Read()) Process();
  return 0;
}
