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;
pair<int, int> foo(string a[], int n) {
  pair<int, int> p = {0, 0};
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + j) % 2 == 0) {
        if (a[i][j] == '1')
          p.first++;
        else
          p.second++;
      } else {
        if (a[i][j] == '1')
          p.second++;
        else
          p.first++;
      }
    }
  }
  return p;
}
int main() {
  int n;
  cin >> n;
  string a1[n];
  string a2[n];
  string a3[n];
  string a4[n];
  for (int i = 0; i < n; ++i) cin >> a1[i];
  for (int i = 0; i < n; ++i) cin >> a2[i];
  for (int i = 0; i < n; ++i) cin >> a3[i];
  for (int i = 0; i < n; ++i) cin >> a4[i];
  vector<pair<int, int>> v;
  v.push_back(foo(a1, n));
  v.push_back(foo(a2, n));
  v.push_back(foo(a3, n));
  v.push_back(foo(a4, n));
  int ans = INT_MAX;
  int curr = 0;
  for (int i = 0; i < 4; ++i) {
    for (int j = i + 1; j < 4; ++j) {
      curr = 0;
      for (int k = 0; k < 4; ++k) {
        if (k == i || k == j)
          curr += v[k].first;
        else
          curr += v[k].second;
      }
      ans = min(ans, curr);
    }
  }
  for (int i = 0; i < 4; ++i) {
    for (int j = i + 1; j < 4; ++j) {
      curr = 0;
      for (int k = 0; k < 4; ++k) {
        if (k == i || k == j)
          curr += v[k].second;
        else
          curr += v[k].first;
      }
      ans = min(ans, curr);
    }
  }
  cout << ans;
  return 0;
}
