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;
template <typename S, typename T>
ostream& operator<<(ostream& out, pair<S, T> const& p) {
  out << '(' << p.first << ", " << p.second << ')';
  return out;
}
template <typename T>
ostream& operator<<(ostream& out, vector<T> const& v) {
  long long l = v.size();
  for (long long i = 0; i < l - 1; i++) out << v[i] << ' ';
  if (l > 0) out << v[l - 1];
  return out;
}
template <typename T>
void trace(const char* name, T&& arg1) {
  cout << name << " : " << arg1 << "\n";
}
template <typename T, typename... Args>
void trace(const char* names, T&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  trace(comma + 1, args...);
}
const long long N = 110;
long long arr[5][N][N];
long long n;
vector<long long> perm = {1, 2, 3, 4};
long long A[2 * N + 100][2 * N + 100];
long long B[2 * N + 100][2 * N + 100];
long long get(long long s) {
  for (long long i = 1; i <= 2 * n; i++) {
    long long temp = s;
    for (long long j = 1; j <= 2 * n; j++) {
      A[i][j] = temp;
      temp ^= 1;
    }
    s ^= 1;
  }
  long long cnt = 0;
  for (long long i = 1; i <= 2 * n; i++) {
    for (long long j = 1; j <= 2 * n; j++) {
      cnt += (A[i][j] != B[i][j]);
    }
  }
  return cnt;
}
long long get_ans() {
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      A[i][j] = B[i][j] = arr[perm[0]][i][j];
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = n + 1; j <= 2 * n; j++) {
      A[i][j] = B[i][j] = arr[perm[1]][i][j - n];
    }
  }
  for (long long i = n + 1; i <= 2 * n; i++) {
    for (long long j = 1; j <= n; j++) {
      A[i][j] = B[i][j] = arr[perm[2]][i - n][j];
    }
  }
  for (long long i = n + 1; i <= 2 * n; i++) {
    for (long long j = n + 1; j <= 2 * n; j++) {
      A[i][j] = B[i][j] = arr[perm[3]][i - n][j - n];
    }
  }
  long long temp = get(1);
  for (long long i = 1; i <= 2 * n; i++) {
    for (long long j = 1; j <= 2 * n; j++) {
      A[i][j] = B[i][j];
    }
  }
  long long temp2 = get(0);
  temp = min(temp, temp2);
  return temp;
}
int32_t main() {
  cin >> n;
  for (long long i = 1; i <= 4; i++) {
    for (long long j = 1; j <= n; j++) {
      string temp;
      cin >> temp;
      for (long long k = 1; k <= n; k++) {
        arr[i][j][k] = temp[k - 1] - '0';
      }
    }
  }
  long long ans = 1000000000000000001;
  do {
    ans = min(ans, get_ans());
  } while (next_permutation(perm.begin(), perm.end()));
  cout << ans << "\n";
}
