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: Akshay Miterani
 * DA-IICT
 */
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {

	static double eps=(double)1e-6;
	static long mod=(long)1e9+7;
	static ArrayList<ArrayList<String>> arr=new ArrayList<>();
	static int i=0;
	public static void main(String args[]) throws FileNotFoundException{
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		//----------------My Code------------------
		Pair p[]=new Pair[4];
		p[0]=new Pair(in.nextInt(), in.nextInt());
		p[1]=new Pair(in.nextInt(), in.nextInt());
		p[2]=new Pair(in.nextInt(), in.nextInt());
		ArrayList<Pair> ans=new ArrayList<>();
		if(isval((p[0].x+p[1].x-p[2].x)) && isval((p[0].y+p[1].y-p[2].y))){
			ans.add(new Pair((p[0].x+p[1].x-p[2].x), (p[0].y+p[1].y-p[2].y)));
		}
		if(isval((p[0].x+p[2].x-p[1].x)) && isval((p[0].y+p[2].y-p[1].y))){
			ans.add(new Pair((p[0].x+p[2].x-p[1].x), (p[0].y+p[2].y-p[1].y)));
		}
		if(isval((p[2].x+p[1].x-p[0].x)) && isval((p[2].y+p[1].y-p[0].y))){
			ans.add(new Pair((p[2].x+p[1].x-p[0].x), (p[2].y+p[1].y-p[0].y)));
		}
		System.out.println(ans.size());
		for(Pair pr:ans){
			out.println(pr.x+" "+pr.y);
		}
		out.close();
		//----------------The End------------------

	}
	static boolean isval(int x){
		return true;
	}
	static boolean my(Pair p[]){
		if(basic(p)){
			return false;
		}
		if(p[0].x+p[2].x==p[1].x+p[3].x){
			if(p[0].y+p[2].y==p[1].y+p[3].y){
				return true;
			}
		}
		if(p[0].x+p[1].x==p[2].x+p[3].x){
			if(p[0].y+p[1].y==p[2].y+p[3].y){
				return true;
			}
		}
		if(p[0].x+p[3].x==p[1].x+p[2].x){
			if(p[0].y+p[3].y==p[1].y+p[2].y){
				return true;
			}
		}
		return false;
	}
	static boolean basic(Pair p[]){
		boolean ok=false;
		ok|=collinear(p[0].x, p[0].y, p[1].x, p[1].y, p[2].x, p[2].y);
		ok|=collinear(p[0].x, p[0].y, p[1].x, p[1].y, p[3].x, p[3].y);
		ok|=collinear(p[0].x, p[0].y, p[2].x, p[2].y, p[3].x, p[3].y);
		ok|=collinear(p[3].x, p[3].y, p[1].x, p[1].y, p[2].x, p[2].y);
		return ok;
	}
	static boolean collinear(int x1, int y1, int x2, int y2, int x3, int y3) {
		return (y1 - y2) * (x1 - x3) == (y1 - y3) * (x1 - x2);
	}
	static boolean allCheck(Pair p[]){
		boolean ok=false;
		for(int i1=0;i1<4;i1++){
			for(int i2=0;i2<4;i2++){
				for(int i3=0;i3<4;i3++){
					for(int i4=0;i4<4;i4++){
						boolean v[]=new boolean[4];
						v[i1]=true;v[i2]=true;v[i3]=true;v[i4]=true;
						if(v[0] && v[1] && v[2] && v[3]){
							ok|=check(p[i1], p[i2], p[i3], p[i4]);
						}
					}
				}
			}
		}
		return ok;
	}
	static boolean check(Pair p1, Pair p2, Pair p3, Pair p4){
		Pair p[]=new Pair[4];
		p[0]=new Pair(-1, -1);p[1]=new Pair(-1, -1);p[2]=new Pair(-1, -1);p[3]=new Pair(-1, -1);
		p[0].x=p2.x-p1.x;p[0].y=p2.y-p1.y;
		p[1].x=p3.x-p2.x;p[1].y=p3.y-p2.y;
		p[2].x=p4.x-p3.x;p[2].y=p4.y-p3.y;
		p[3].x=p1.x-p4.x;p[3].y=p1.y-p4.y;
		return (p[0].x==p[2].x && p[0].y==p[2].y) && (p[1].x==p[3].x && p[1].y==p[3].y);
	}
	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;
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;

		Pair(int xx,int yy){
			x=xx;
			y=yy;
		}
		@Override
		public int compareTo(Pair o) {
			if(Long.compare(this.y, o.y)!=0)
				return Long.compare(this.y, o.y);
			else
				return Long.compare(this.x, o.x);
		}
	}
	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	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());
		}
	}
}