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 double eps = 1e-7, PI = 3.1415926;
const int N = 1e6;
using namespace std;
long long q, n, m, k, x, a[N], sum, mx = -1, mn = 1e9;
string c[4][110];
string s;
vector<int> vec[N];
map<long long, long long> M0;
map<long long, long long> M1;
int main() {
  scanf("%d", &n);
  for (int j = 0; j < 4; j++) {
    for (int i = 0; i < n; i++) {
      cin >> c[j][i];
    }
  }
  for (int j = 0; j < 4; j++) {
    for (int i = 0; i < n; i++) {
      for (int y = 0; y < n; y++) {
        if (i % 2 == y % 2)
          x = 0;
        else
          x = 1;
        if (c[j][i][y] - 48 != x) M0[j]++;
      }
    }
  }
  for (int j = 0; j < 4; j++) {
    for (int i = 0; i < n; i++) {
      for (int y = 0; y < n; y++) {
        if (i % 2 == y % 2)
          x = 1;
        else
          x = 0;
        if (c[j][i][y] - 48 != x) M1[j]++;
      }
    }
  }
  vec[0].push_back(M0[0] + M0[1]);
  vec[0].push_back(M0[0] + M0[2]);
  vec[0].push_back(M0[0] + M0[3]);
  vec[0].push_back(M0[1] + M0[2]);
  vec[0].push_back(M0[1] + M0[3]);
  vec[0].push_back(M0[2] + M0[3]);
  vec[1].push_back(M1[2] + M1[3]);
  vec[1].push_back(M1[1] + M1[3]);
  vec[1].push_back(M1[1] + M1[2]);
  vec[1].push_back(M1[0] + M1[3]);
  vec[1].push_back(M1[0] + M1[2]);
  vec[1].push_back(M1[0] + M1[1]);
  for (int i = 0; i < vec[0].size(); i++) {
    k = vec[0][i] + vec[1][i];
    mn = min(mn, k);
  }
  cout << mn;
}
