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.*;
import java.util.*;
import java.lang.*;
    public class templ {
    int binarySearch(int arr[], int l, int r, int x)
    {
        if (r >= l)
        {
            int mid = l + (r - l)/2;
            if (arr[mid] == x)
            return mid;
            if (arr[mid] > x) 
            return binarySearch(arr, l, mid-1, x);
            return binarySearch(arr, mid+1, r, x);
        }
        return -1;
    }
    int partition(int arr[], int low, int high)
    {
        int pivot = arr[high]; 
        int i = (low-1);
        for (int j=low; j<high; j++)
        {
            if (arr[j] <= pivot)
            {
                i++;
                int temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
                //temp=a[high];
                //a[i]=a[j];
                //a[j]=temp;
            }
        }
        int temp = arr[i+1];
        arr[i+1] = arr[high];
        arr[high] = temp;
        //temp=a[i+1];
        //a[i+1]=a[high];
        //a[high]=temp;
        return i+1;
    }
    void sort(int arr[], int low, int high)
    {
        if (low < high)
        {
            int pi = partition(arr, low, high);
            sort(arr, low, pi-1);
            sort(arr, pi+1, high);
        }
    }
    int costofone(String s[],int n)
    {
        int cost=0;
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                char c=s[i].charAt(j);
                if(i%2==0&&j%2==0&&c=='0')
                    cost++;
                else if(i%2==0&&j%2==1&&c=='1')
                    cost++;
                else if(i%2==1&&j%2==0&&c=='1')
                    cost++;
                else if(i%2==1&&j%2==1&&c=='0')
                    cost++;
            }
        }
        return cost;
    }
    int costofzero(String s[],int n)
    {
        int cost=0;
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                char c=s[i].charAt(j);
                if(i%2==0&&j%2==0&&c=='1')
                    cost++;
                else if(i%2==0&&j%2==1&&c=='0')
                    cost++;
                else if(i%2==1&&j%2==0&&c=='0')
                    cost++;
                else if(i%2==1&&j%2==1&&c=='1')
                    cost++;
            }
        }
        return cost;
    }
    public static void main(String[] args) throws FileNotFoundException {
     try
     {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        templ ob=new templ();
        int n=in.nextInt();
        int c0[]=new int[4];
        int c1[]=new int[4];
        for(int i=0;i<4;i++)
        {
            String s[]=new String[n];
            for(int j=0;j<n;j++)
            {
                s[j]=in.nextLine();
            }
            c0[i]=ob.costofzero(s,n);
            c1[i]=ob.costofone(s,n);
        }
        int cost[]=new int[6];
        cost[0]=c0[0]+c0[1]+c1[2]+c1[3];
        cost[1]=c0[0]+c1[1]+c0[2]+c1[3];
        cost[2]=c0[0]+c1[1]+c1[2]+c0[3];
        cost[3]=c1[0]+c0[1]+c0[2]+c1[3];
        cost[4]=c1[0]+c0[1]+c1[2]+c0[3];
        cost[5]=c1[0]+c1[1]+c0[2]+c0[3];
        int mincost=100000000;
        for(int i=0;i<6;i++)
        {
            if(mincost>cost[i])
                mincost=cost[i];
        }
        out.println(mincost);
        out.close();
    }
        catch(Exception e){
        return;
    }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
} 	