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;
using ll = long long;
using vi = vector<long long>;
using pii = pair<long long, long long>;
const signed INF_ = 1001001001;
const long long INF = 1001001001001001001LL;
const long long DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
                DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto i = (begin(v)); i != (end(v)); ++i)
    os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto i = (begin(v)); i != (end(v)); ++i) is >> *i;
  return is;
}
template <class T, class U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
using heap = priority_queue<T, vector<T>, greater<T>>;
struct {
  template <class T>
  operator T() {
    T x;
    cin >> x;
    return x;
  }
} IN;
struct before_main_function {
  before_main_function() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
  }
} before_main_function;
signed main() {
  long long n;
  cin >> n;
  vector<pii> dist(4, {0, 0});
  for (long long b = 0, blen = (long long)(4); b < blen; ++b) {
    for (long long i = 0, ilen = (long long)(n); i < ilen; ++i) {
      string s;
      cin >> s;
      for (long long j = 0, jlen = (long long)(n); j < jlen; ++j) {
        if ((i + j) % 2) {
          if (s[j] == '1') dist[b].first++;
          if (s[j] == '0') dist[b].second++;
        } else {
          if (s[j] == '0') dist[b].first++;
          if (s[j] == '1') dist[b].second++;
        }
      }
    }
  }
  long long ans = INF;
  for (long long i = 0, ilen = (long long)(1 << 4); i < ilen; ++i) {
    if (__builtin_popcount(i) != 2) continue;
    long long tmp = 0;
    for (long long j = 0, jlen = (long long)(4); j < jlen; ++j) {
      if ((i >> j) & 1) {
        tmp += dist[j].first;
      } else {
        tmp += dist[j].second;
      }
    }
    chmin(ans, tmp);
  }
  cout << ans << "\n";
  return 0;
}
