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 m[4][110][110];
int n;
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, -1, 1};
bool vis[100][100];
inline bool valida(int x, int y) {
  return (x > -1 && y > -1 && n > x && n > y && vis[x][y] == 0);
}
int TANTO;
void arruma(int Q, int cor, int x, int y) {
  vis[x][y] = 1;
  if (cor != m[Q][x][y]) TANTO++;
  for (int i = 0; i < 4; ++i) {
    int xx = dx[i] + x, yy = dy[i] + y;
    if (valida(xx, yy)) {
      arruma(Q, !cor, xx, yy);
    }
  }
}
int qtd[4][2];
int ANS;
void f(int idx, int b, int p, int temp) {
  if (p == 3 || p == 3) return;
  if (idx == 4) {
    if (b == 2 && p == 2) ANS = min(ANS, temp);
    return;
  }
  f(idx + 1, b + 1, p, temp + qtd[idx][0]);
  f(idx + 1, b, p + 1, temp + qtd[idx][1]);
}
int main() {
  cin >> n;
  for (int i = 0; i < 4; ++i) {
    for (int l = 0; l < n; ++l) {
      string s;
      cin >> s;
      for (int c = 0; c < n; ++c) {
        m[i][l][c] = s[c] - '0';
      }
    }
  }
  for (int i = 0; i < 4; ++i) {
    TANTO = 0;
    memset(vis, 0, sizeof vis);
    arruma(i, 1, 0, 0);
    qtd[i][0] = TANTO;
    TANTO = 0;
    memset(vis, 0, sizeof vis);
    arruma(i, 0, 0, 0);
    qtd[i][1] = TANTO;
  }
  ANS = 1e9 + 100;
  f(0, 0, 0, 0);
  cout << ANS << '\n';
  return 0;
}
