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 const N = 5e5 + 10;
int mod = 1e9 + 7;
int x, t, y, z, n, m, q, k, ans;
vector<int> v;
char s1[100][100], s2[100][100], s3[100][100], s4[100][100];
char arr[205][205];
int dx[4] = {0, 0, 1, -1};
int dy[4] = {1, -1, 0, 0};
int frq1[400], frq2[400];
int calc(int a, int b, int c, int d) {
  for (int i = 0, ii = 0; i < n; i++, ii++) {
    for (int j = 0, jj = 0; j < n; j++, jj++) {
      if (a == 1) {
        arr[i][j] = s1[ii][jj];
      }
      if (a == 2) {
        arr[i][j] = s2[ii][jj];
      }
      if (a == 3) {
        arr[i][j] = s3[ii][jj];
      }
      if (a == 4) {
        arr[i][j] = s4[ii][jj];
      }
    }
  }
  for (int i = 0, ii = 0; i < n; i++, ii++) {
    for (int j = n, jj = 0; j < 2 * n; j++, jj++) {
      if (b == 1) {
        arr[i][j] = s1[ii][jj];
      }
      if (b == 2) {
        arr[i][j] = s2[ii][jj];
      }
      if (b == 3) {
        arr[i][j] = s3[ii][jj];
      }
      if (b == 4) {
        arr[i][j] = s4[ii][jj];
      }
    }
  }
  for (int i = n, ii = 0; i < 2 * n; i++, ii++) {
    for (int j = 0, jj = 0; j < n; j++, jj++) {
      if (c == 1) {
        arr[i][j] = s1[ii][jj];
      }
      if (c == 2) {
        arr[i][j] = s2[ii][jj];
      }
      if (c == 3) {
        arr[i][j] = s3[ii][jj];
      }
      if (c == 4) {
        arr[i][j] = s4[ii][jj];
      }
    }
  }
  for (int i = n, ii = 0; i < 2 * n; ii++, i++) {
    for (int j = n, jj = 0; j < 2 * n; j++, jj++) {
      if (d == 1) {
        arr[i][j] = s1[ii][jj];
      }
      if (d == 2) {
        arr[i][j] = s2[ii][jj];
      }
      if (d == 3) {
        arr[i][j] = s3[ii][jj];
      }
      if (d == 4) {
        arr[i][j] = s4[ii][jj];
      }
    }
  }
  int count = 0;
  for (int i = 0; i < 400; i++) {
    frq1[i] = frq2[i] = 0;
  }
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if (arr[i][j] == '1')
        frq1[i + j]++;
      else
        frq2[i + j]++;
    }
  }
  int ans1 = 0, ans2 = 0;
  for (int i = 0; i < 400; i++) {
    if (i % 2 == 0) {
      ans1 += frq2[i];
    } else {
      ans1 += frq1[i];
    }
  }
  for (int i = 0; i < 400; i++) {
    if (i % 2 == 0) {
      ans2 += frq1[i];
    } else {
      ans2 += frq2[i];
    }
  }
  return min(ans1, ans2);
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s1[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s2[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s3[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s4[i][j];
    }
  }
  ans = 1e9;
  string str = "1234";
  vector<int> lo;
  lo.resize(4);
  lo[0] = 1;
  lo[1] = 2;
  lo[2] = 3;
  lo[3] = 4;
  do {
    k = calc(lo[0], lo[1], lo[2], lo[3]);
    ans = min(ans, k);
  } while (next_permutation(lo.begin(), lo.end()));
  cout << ans << endl;
  return 0;
}
