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.util.*;
import java.io.*;
import java.math.*;

public class c {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        ArrayList<StringBuffer> a = new ArrayList<StringBuffer>();
        ArrayList<StringBuffer> b = new ArrayList<StringBuffer>();
        ArrayList<StringBuffer> c = new ArrayList<StringBuffer>();
        ArrayList<StringBuffer> d = new ArrayList<StringBuffer>();

        readinput(in, a, n);
        readinput(in, b, n);
        readinput(in, c, n);
        readinput(in, d, n);

        // First conf should be a b \n c d
        ArrayList<StringBuffer> conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + d.get(i).toString()));

        int min = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + c.get(i).toString()));

        int flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        // Second Conf
        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + d.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + c.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + d.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + c.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + d.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + c.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + d.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + d.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + d.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + c.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + a.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + c.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + b.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(c.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(a.get(i).toString() + b.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        conf1 = new ArrayList<StringBuffer>();
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(d.get(i).toString() + c.get(i).toString()));
        for(int i = 0; i < n; i++)
            conf1.add(new StringBuffer(b.get(i).toString() + a.get(i).toString()));

        flips = Math.min(getNumberOfFlips('0', conf1), getNumberOfFlips('1', conf1));
        if(flips < min)
            min = flips;

        System.out.println(min);
    }

    public static void readinput(Scanner in, ArrayList<StringBuffer> a, int n) {
        for(int i = 0; i < n; i++)
            a.add(new StringBuffer(in.next()));
    }

    public static int getNumberOfFlips(char starting, ArrayList<StringBuffer> a) {
        ArrayList<StringBuffer> toCompare = new ArrayList<StringBuffer>();
        for(int i = 0; i < a.size(); i++) {
            toCompare.add(new StringBuffer());
            if(starting == '0' && i % 2 == 0)
                for(int j = 0; j < a.size(); j++)
                    if(j%2 == 0)
                        toCompare.get(i).append("0");
                    else
                        toCompare.get(i).append("1");

            else if(starting == '1' && i % 2 == 0)
                for(int j = 0; j < a.size(); j++)
                    if(j % 2 == 0)
                        toCompare.get(i).append("1");
                    else
                        toCompare.get(i).append("0");

            else if(starting == '0' && i % 2 == 1)
                for(int j = 0; j < a.size(); j++)
                    if(j%2 == 0)
                        toCompare.get(i).append("1");
                    else
                        toCompare.get(i).append("0");

            else if(starting == '1' && i % 2 == 1)
                for(int j = 0; j < a.size(); j++)
                    if(j%2 == 0)
                        toCompare.get(i).append("0");
                    else
                        toCompare.get(i).append("1");
        }
        int flips = 0;
        for(int i = 0; i < a.size(); i++) {
            String orig = a.get(i).toString();
            String shouldbe = toCompare.get(i).toString();
            for(int j = 0; j < orig.length(); j++)
                if(orig.charAt(j) != shouldbe.charAt(j))
                    flips++;
        }
        return flips;
    }
}
