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 maxn = 105;
int n, ans;
int data[4][maxn][maxn];
int cal() {
  int chi[2][4], ret = 0;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 4; j++) {
      int sum = 0;
      for (int ii = 0; ii < n; ii++) {
        for (int jj = 0; jj < n; jj++) {
          int res = (ii + jj) % 2;
          if (i == 0) {
            if (data[j][ii][jj] != res) sum++;
          } else {
            if (data[j][ii][jj] == res) sum++;
          }
        }
      }
      chi[i][j] = sum;
    }
  }
  int A[4], B[4];
  for (int i = 0; i < 4; i++) {
    A[i] = abs(chi[0][i] - chi[1][i]);
    B[i] = i;
  }
  for (int i = 3; i > 0; i--) {
    for (int j = 0; j < i; j++) {
      if (A[j] < A[j + 1]) {
        int tmp = A[j];
        A[j] = A[j + 1];
        A[j + 1] = tmp;
        tmp = B[j];
        B[j] = B[j + 1];
        B[j + 1] = tmp;
      }
    }
  }
  int ones = 0, zeros = 0;
  if (chi[0][B[0]] < chi[1][B[0]]) {
    zeros++;
    ret += chi[0][B[0]];
  } else {
    ones++;
    ret += chi[1][B[0]];
  }
  if (chi[0][B[1]] < chi[1][B[1]]) {
    zeros++;
    ret += chi[0][B[1]];
  } else {
    ones++;
    ret += chi[1][B[1]];
  }
  if (ones == 2) {
    ret += chi[0][B[2]];
    ret += chi[0][B[3]];
  } else if (zeros == 2) {
    ret += chi[1][B[2]];
    ret += chi[1][B[3]];
  } else {
    if (chi[0][B[2]] < chi[1][B[2]]) {
      ret += chi[0][B[2]];
      ret += chi[1][B[3]];
    } else {
      ret += chi[1][B[2]];
      ret += chi[0][B[3]];
    }
  }
  return ret;
}
int main(void) {
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        char x;
        cin >> x;
        while (x != '0' && x != '1') cin >> x;
        data[i][j][k] = x - '0';
      }
    }
  }
  cout << cal() << endl;
  return 0;
}
