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;
bool check(string a[], int n) {
  int t;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (!i && !j)
        t = a[i][j];
      else {
        if (a[i][j] == t)
          return 0;
        else
          t = a[i][j];
      }
    }
  }
  return 1;
}
int correct(string a[], int n) {
  int t, c = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (!i && !j)
        t = a[i][j];
      else {
        if (a[i][j] == t) {
          a[i][j] = !(t - '0') + '0';
          c++;
          t = a[i][j];
        } else
          t = a[i][j];
      }
    }
  }
  return c;
}
bool comp(pair<int, int> a, pair<int, int> b) {
  if (a.first < b.first)
    return 1;
  else
    return 0;
}
int main() {
  int n;
  cin >> n;
  string a[n], b[n], c[n], d[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) cin >> b[i];
  for (int i = 0; i < n; i++) cin >> c[i];
  for (int i = 0; i < n; i++) cin >> d[i];
  bool val[4];
  val[0] = check(a, n);
  val[1] = check(b, n);
  val[2] = check(c, n);
  val[3] = check(d, n);
  int x, y, z, w;
  x = y = z = w = 0;
  if (!val[0]) {
    x = correct(a, n);
  }
  if (!val[1]) {
    y = correct(b, n);
  }
  if (!val[2]) {
    z = correct(c, n);
  }
  if (!val[3]) {
    w = correct(d, n);
  }
  vector<pair<int, int>> v;
  v.push_back(make_pair(x, a[0][0]));
  v.push_back(make_pair(y, b[0][0]));
  v.push_back(make_pair(z, c[0][0]));
  v.push_back(make_pair(w, d[0][0]));
  v.push_back(make_pair(n * n - x, !(a[0][0] - '0') + '0'));
  v.push_back(make_pair(n * n - y, !(b[0][0] - '0') + '0'));
  v.push_back(make_pair(n * n - z, !(c[0][0] - '0') + '0'));
  v.push_back(make_pair(n * n - w, !(d[0][0] - '0') + '0'));
  sort(v.begin(), v.end(), comp);
  int ones[4], zeros[4], q = 0, e = 0;
  for (int i = 0; i < 8; i++) {
    if (v[i].second == '0')
      zeros[e++] = i;
    else
      ones[q++] = i;
  }
  cout << v[ones[0]].first + v[ones[1]].first + v[zeros[0]].first +
              v[zeros[1]].first;
}
