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;
long long int GCD(long long int x, long long int y) {
  if (y == 0) return x;
  return GCD(y, x % y);
}
vector<bool> seive_Of_Eratosthenes(long long int n) {
  vector<bool> prime(n + 1, true);
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) {
        prime[i] = false;
      }
    }
  }
  return prime;
}
long long int power(long long int x, long long int y) {
  long long int ans = 1;
  while (y > 0) {
    if (y % 2 == 1) {
      ans = ans * x;
    }
    y = (y >> 1);
    x = x * x;
  }
  return ans;
}
bool isSquare(long long int n) {
  long long int sq = sqrt(n);
  if (sq * sq == n) {
    return true;
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  vector<string> v;
  bool one = true;
  for (int i = 0; i < n; i++) {
    string s = "";
    if (one)
      s += '1';
    else
      s += '0';
    for (int j = 1; j < n; j++) {
      if (s[j - 1] == '0') {
        s += '1';
      } else {
        s += '0';
      }
    }
    one = (!one);
    v.push_back(s);
  }
  vector<string> v1;
  one = false;
  for (int i = 0; i < n; i++) {
    string s = "";
    if (one)
      s += '1';
    else
      s += '0';
    for (int j = 1; j < n; j++) {
      if (s[j - 1] == '0') {
        s += '1';
      } else {
        s += '0';
      }
    }
    one = (!one);
    v1.push_back(s);
  }
  string str;
  vector<string> in1;
  for (int i = 0; i < n; i++) {
    cin >> str;
    in1.push_back(str);
  }
  vector<string> in2;
  for (int i = 0; i < n; i++) {
    cin >> str;
    in2.push_back(str);
  }
  vector<string> in3;
  for (int i = 0; i < n; i++) {
    cin >> str;
    in3.push_back(str);
  }
  vector<string> in4;
  for (int i = 0; i < n; i++) {
    cin >> str;
    in4.push_back(str);
  }
  vector<int> t1;
  vector<int> t2;
  int nm1 = 0, nm2 = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in1[i][j] != v[i][j]) {
        nm1++;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in1[i][j] != v1[i][j]) {
        nm2++;
      }
    }
  }
  t1.push_back(nm1);
  t2.push_back(nm2);
  nm1 = 0;
  nm2 = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in2[i][j] != v[i][j]) {
        nm1++;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in2[i][j] != v1[i][j]) {
        nm2++;
      }
    }
  }
  t1.push_back(nm1);
  t2.push_back(nm2);
  nm1 = 0;
  nm2 = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in3[i][j] != v[i][j]) {
        nm1++;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in3[i][j] != v1[i][j]) {
        nm2++;
      }
    }
  }
  t1.push_back(nm1);
  t2.push_back(nm2);
  nm1 = 0;
  nm2 = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in4[i][j] != v[i][j]) {
        nm1++;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (in4[i][j] != v1[i][j]) {
        nm2++;
      }
    }
  }
  t1.push_back(nm1);
  t2.push_back(nm2);
  sort(t1.begin(), t1.end());
  sort(t2.begin(), t2.end());
  cout << t1[0] + t1[1] + t2[0] + t2[1] << "\n";
  return 0;
}
