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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.BitSet;

public class Solution {

    public static void main(String[] args) throws IOException {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            String l1 = br.readLine();
            int n = Integer.parseInt(l1.trim());

            int sz = n * n;

            BitSet[] colors = new BitSet[] {
                    new BitSet(sz),
                    new BitSet(sz),
                    new BitSet(sz),
                    new BitSet(sz)
            };

            for (int i = 0; i < 4; i++) {
                BitSet bitSet = colors[i];
                for (int l = 0; l < n; l++) {
                    String s = br.readLine();
                    String[] parts = s.split("");
                    for (int k = 0; k < n; k++) {
                        int idx = l * n + k;
                        if (parts[k].equals("1")) {
                            bitSet.set(idx);
                        }
                    }
                }
                if (i < 3) {
                    br.readLine();
                }
            }

            BitSet direct = new BitSet(sz);
            for (int i = 0; i < sz; i += 2) {
                direct.set(i);
            }
            BitSet reverse = (BitSet) direct.clone();
            reverse.flip(0, sz);

            BitSet tmpDirect = new BitSet(sz);
            tmpDirect.or(direct);
            BitSet tmpReverse = new BitSet(sz);
            tmpReverse.or(reverse);

            int min = Integer.MAX_VALUE;

            for (int i = 0; i < 4; i++) {
                for (int j = i + 1; j < 4; j++) {
                    for (int p = 0; p < 4; p++) {
                        if (p == i || p == j) {
                            continue;
                        }
                        for (int q = p + 1; q < 4; q++) {
                            if (q == i || q == j) {
                                continue;
                            }
                            BitSet bs1 = colors[i];
                            tmpDirect.xor(bs1);
                            int ones = tmpDirect.cardinality();

                            BitSet bs2 = colors[j];
                            tmpDirect.xor(bs1);
                            tmpDirect.xor(bs2);
                            ones += tmpDirect.cardinality();
                            tmpDirect.xor(bs2);

                            BitSet bs3 = colors[p];
                            tmpReverse.xor(bs3);
                            ones += tmpReverse.cardinality();

                            BitSet bs4 = colors[q];
                            tmpReverse.xor(bs3);
                            tmpReverse.xor(bs4);
                            ones += tmpReverse.cardinality();
                            tmpReverse.xor(bs4);

                            if (ones < min) {
                                min = ones;
                            }
                        }
                    }
                }
            }

            System.out.println(min);
        }
    }
}