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;
const int N = 210;
int n, a[5][N][N], b[N][N], p[5], ans = N * N, m;
bool vis[N][N];
char S[N];
inline int gi() {
  int x = 0, res = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') res ^= ch == '-', ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - 48, ch = getchar();
  return res ? x : -x;
}
inline int dfs(int x, int y, bool c) {
  if (vis[x][y]) return 0;
  vis[x][y] = 1;
  int tot = c == b[x][y] ? 0 : 1;
  if (x > 1) tot += dfs(x - 1, y, c ^ 1);
  if (x < m) tot += dfs(x + 1, y, c ^ 1);
  if (y > 1) tot += dfs(x, y - 1, c ^ 1);
  if (y < m) tot += dfs(x, y + 1, c ^ 1);
  return tot;
}
inline void calc() {
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j) b[i][j] = a[p[1]][i][j];
  for (int i = 1; i <= n; ++i)
    for (int j = n + 1; j <= m; ++j) b[i][j] = a[p[2]][i][j - n];
  for (int i = n + 1; i <= m; ++i)
    for (int j = 1; j <= n; ++j) b[i][j] = a[p[3]][i - n][j];
  for (int i = n + 1; i <= m; ++i)
    for (int j = n + 1; j <= m; ++j) b[i][j] = a[p[4]][i - n][j - n];
  memset(vis, 0, sizeof(vis));
  ans = min(ans, dfs(1, 1, 0));
  memset(vis, 0, sizeof(vis));
  ans = min(ans, dfs(1, 1, 1));
}
int main() {
  n = gi();
  m = n << 1;
  for (int k = 1; k <= 4; ++k)
    for (int i = 1; i <= n; ++i) {
      scanf("%s", S + 1);
      for (int j = 1; j <= n; ++j) a[k][i][j] = S[j] - 48;
    }
  for (int i = 1; i <= 4; ++i) p[i] = i;
  do {
    calc();
  } while (next_permutation(p + 1, p + 5));
  cout << ans << endl;
  return 0;
}
