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;
int dis_A(vector<vector<char> >);
int dis_B(vector<vector<char> >);
int main() {
  int n;
  cin >> n;
  vector<vector<char> > mat1(n, vector<char>(n)), mat2(n, vector<char>(n)),
      mat3(n, vector<char>(n)), mat4(n, vector<char>(n));
  vector<int> A(4), B(4), sum;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> mat1[i][j];
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> mat2[i][j];
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> mat3[i][j];
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> mat4[i][j];
  A[0] = dis_A(mat1);
  A[1] = dis_A(mat2);
  A[2] = dis_A(mat3);
  A[3] = dis_A(mat4);
  B[0] = dis_B(mat1);
  B[1] = dis_B(mat2);
  B[2] = dis_B(mat3);
  B[3] = dis_B(mat4);
  for (int i = 0; i < 4; ++i)
    for (int j = 0; j < i; ++j) {
      int temp = A[i] + A[j];
      for (int k = 0; k < 4; ++k) {
        if (k != i && k != j) temp += B[k];
      }
      sum.push_back(temp);
    }
  int min = *min_element(sum.begin(), sum.end());
  cout << min;
}
int dis_A(vector<vector<char> > mat) {
  int n = mat.size();
  int sum = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + j) % 2 == 0)
        sum += abs(int(mat[i][j]) - int('1'));
      else
        sum += abs(int(mat[i][j]) - int('0'));
    }
  }
  return sum;
}
int dis_B(vector<vector<char> > mat) {
  int n = mat.size();
  int sum = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i + j) % 2 == 0)
        sum += abs(int(mat[i][j]) - int('0'));
      else
        sum += abs(int(mat[i][j]) - int('1'));
    }
  }
  return sum;
}
