Problem: Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.

Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.

Input

The input consists of three lines, each containing a pair of integer coordinates xi and yi ( - 1000 ≤ xi, yi ≤ 1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.

Output

First print integer k — the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices.

Then print k lines, each containing a pair of integer — possible coordinates of the fourth point.

Example

Input

0 0
1 0
0 1


Output

3
1 -1
-1 1
1 1

Note

If you need clarification of what parallelogram is, please check Wikipedia page:

https://en.wikipedia.org/wiki/Parallelogram

Solution (in JAVA):

Solution:
// Code Author: Rutul Patel
 
import java.io.*;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;
public class Main {

	static double eps=(double)1e-6;
	static long mod=(int)1e9+6;
	public static void main(String args[]){
		InputReader sc = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		//----------My Code----------
		
		int x1=sc.nextInt();
		int y1=sc.nextInt();
		int x2=sc.nextInt();
		int y2=sc.nextInt();
		int x3=sc.nextInt();
		int y3=sc.nextInt();
		
		int ax1=x2+x3-x1;
		int ay1=y2+y3-y1;
		int ax2=x1+x3-x2;
		int ay2=y1+y3-y2;
		int ax3=x1+x2-x3;
		int ay3=y1+y2-y3;
		
		out.println(3);
		out.println(ax1+" "+ay1);
		out.println(ax2+" "+ay2);
		out.println(ax3+" "+ay3);
		//----------The End----------
		out.close();
	}

	
	static int[] sieve(int n,int[] arr)
	{
		for(int i=2;i*i<=n;i++)
		{
			if(arr[i]==0)
			{
				for(int j=i*2;j<=n;j+=i)
					arr[j]=1;
			}
		}
		return arr;
	}
	
	static boolean isPal(String s)
	{
		for(int i=0, j=s.length()-1;i<=j;i++,j--)
		{
			if(s.charAt(i)!=s.charAt(j)) return false;
		}
		return true;
	}
	public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}
	    
	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}
	
	static long gcd(long a, long b)
	{
	    while (b > 0)
	    {
	        long temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static long modulo(long a,long b,long c) {
		long x=1;
		long y=a;
		while(b > 0){
			if(b%2 == 1){
				x=(x*y)%c;
			}
			y = (y*y)%c; // squaring the base
			b /= 2;
		}
		return  x%c;
	}
	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		int i;
		Pair(int xx,int yy){
			x=xx;
			y=yy;
		}
		public Pair() {
			// TODO Auto-generated constructor stub
		}
		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine(){
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
	
}