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;
ifstream fin(
    ""
    ".in");
ofstream fout(
    ""
    ".out");
int n;
vector<int> a;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  a.resize(n);
  vector<int> r1(4, 0);
  vector<int> r2(4, 0);
  for (int k = 0; k < 4; k++) {
    char curr;
    char good1 = '0';
    char good2 = '1';
    for (int i = 0; i < n * n; i++) {
      cin >> curr;
      if (curr != good1) {
        r1[k]++;
      }
      if (curr != good2) {
        r2[k]++;
      }
      if (good1 == '0') {
        good1 = '1';
        good2 = '0';
      } else {
        good1 = '0';
        good2 = '1';
      }
    }
  }
  int ans = 10000000;
  vector<int> kek(1000, 10000000);
  kek[0] = r1[0] + r1[1] + r2[2] + r2[3];
  kek[1] = r1[0] + r1[1] + r2[3] + r2[2];
  kek[2] = r1[0] + r1[2] + r2[1] + r2[3];
  kek[3] = r1[0] + r1[2] + r2[3] + r2[1];
  kek[4] = r1[0] + r1[3] + r2[1] + r2[2];
  kek[5] = r1[0] + r1[3] + r2[2] + r2[1];
  kek[6] = r1[1] + r1[0] + r2[2] + r2[3];
  kek[7] = r1[1] + r1[0] + r2[3] + r2[2];
  kek[8] = r1[1] + r1[2] + r2[0] + r2[3];
  kek[9] = r1[1] + r1[2] + r2[3] + r2[0];
  kek[10] = r1[1] + r1[3] + r2[0] + r2[2];
  kek[11] = r1[1] + r1[3] + r2[2] + r2[0];
  kek[12] = r1[2] + r1[0] + r2[1] + r2[3];
  kek[13] = r1[2] + r1[0] + r2[3] + r2[1];
  kek[14] = r1[2] + r1[1] + r2[0] + r2[3];
  kek[15] = r1[2] + r1[1] + r2[3] + r2[0];
  kek[16] = r1[2] + r1[3] + r2[0] + r2[1];
  kek[17] = r1[2] + r1[3] + r2[1] + r2[0];
  kek[18] = r1[3] + r1[0] + r2[1] + r2[2];
  kek[19] = r1[3] + r1[0] + r2[2] + r2[1];
  kek[20] = r1[3] + r1[1] + r2[0] + r2[2];
  kek[21] = r1[3] + r1[1] + r2[2] + r2[0];
  kek[22] = r1[3] + r1[2] + r2[0] + r2[1];
  kek[23] = r1[3] + r1[2] + r2[1] + r2[0];
  for (int i = 0; i < 24; i++) {
    if (kek[i] < ans) {
      ans = kek[i];
    }
  }
  cout << ans;
  return 0;
}
