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.*;

public class Main
{		
   public static void main(String[] args) throws java.lang.Exception
   {	  	         
     fast s = new fast();
     PrintWriter out=new PrintWriter(System.out);
     StringBuilder final_ans = new StringBuilder();
    
     int n=s.nextInt();
     int [][] a=new int[n][n];
     int [][] b=new int[n][n];
     
     int c[]=new int[4];
     int d[]=new int[4];
     
     int temp[]=new int[4];
     
     String[] arr=new String[n];
     
     for(int i=0;i<n;i++)
     {
    	 if(i==0) {a[0][0]=0; b[0][0]=1;}
    	 else {a[i][0]=1-a[i-1][0]; b[i][0]=1-b[i-1][0];}
    	 for(int j=1;j<n;j++)
    	 {
    		 a[i][j]=1-a[i][j-1];
    		 b[i][j]=1-b[i][j-1];
    	 }
     }
     
   for(int i=0;i<4;i++)
   {
	 arr=new String[n];
     for(int j=0;j<n;j++)
     {
    	 arr[j]=s.nextLine();
     } 
     
     for(int j=0;j<n;j++)
     {
    	 for(int k=0;k<n;k++)
    	 {
    		 if(arr[j].charAt(k)!=(char)(a[j][k]+'0')) c[i]++;
    		 if(arr[j].charAt(k)!=(char)(b[j][k]+'0')) d[i]++;   			 
    	 }
     }
   }
   
   int sum=0;int ans=Integer.MAX_VALUE;
   
   for(int i=0;i<4;i++)
   {
	   for(int j=0;j<4;j++)
	   {
		   temp=new int[4];
		   if(i==j) continue;
		   sum=c[i]+c[j];
		   temp[i]=1; temp[j]=1;
		   for(int k=0;k<4;k++)
			   if(temp[k]==0)
				   sum+=d[k];
		   
		   ans=Math.min(ans,sum);
	   }
   }
   
   System.out.println(ans);
   
   
   
  }

   
   static class fast {
		private InputStream i;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		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 String nextString() {
     		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 long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}	
}
       
 
   
 


      
   

