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:
import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
 
public class Main implements Runnable {
 
    int maxn = (int)1e5+111;
    int mod = (int)1e9+7;
    int inf = (int)1e9;
    int n,m;
    int a[][] = new int[10][2];
    
    void solve() throws Exception {
    	
    	Point p1 = new Point(in.nextInt(), in.nextInt());
    	Point p2 = new Point(in.nextInt(), in.nextInt());
    	Point p3 = new Point(in.nextInt(), in.nextInt());
    	
    	HashSet<Pair> set = new HashSet<Pair>();
    	set.add(check(p1,p2,p3));
    	set.add(check(p2,p1,p3));
    	set.add(check(p3,p1,p2));
    	
    	out.println(set.size());
    	for (Pair p: set) {
    		out.println(p.x + " " + p.y);
    	}
    }
    
	private Pair check(Point p1, Point p2, Point p3) {
//		p1.x-=p1.x;
//		p1.y-=p1.y;
//		
//		p2.x-=p1.x;
//		p2.y-=p1.y;
//		
//		p3.x-=p1.x;
//		p3.y-=p1.y;
//		
		return new Pair(p2.x+p3.x-p1.x, p2.y+p3.y-p1.y);
	}

	class Pair {
    	int x;
    	int y;
    	public Pair (int x, int y) {
    		this.x = x;
    		this.y = y;
    	}
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + getOuterType().hashCode();
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (!getOuterType().equals(other.getOuterType()))
				return false;
			if (x != other.x)
				return false;
			if (y != other.y)
				return false;
			return true;
		}
		private Main getOuterType() {
			return Main.this;
		}
    	
    	
    }

	String fileInName = "network";
    boolean file = false;
    boolean isAcmp = true;
 
    static Throwable throwable;
    public static void main (String [] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }
 
    FastReader in;
    PrintWriter out;
 
    public void run() {
        String fileIn = "input.txt";
        String fileOut = "output.txt";
 
        try {
            if (isAcmp) {
                if (file) {
                    in = new FastReader(new BufferedReader(new FileReader(fileIn)));
                    out = new PrintWriter (fileOut);
                } else {
                    in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                    out = new PrintWriter(System.out);
                }
            } else if (file) {
                in = new FastReader(new BufferedReader(new FileReader(fileInName+".in")));
                out = new PrintWriter (fileInName + ".out");
            } else {
                in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                out = new PrintWriter(System.out);
            }
 
            solve();
        } catch(Exception e) {
            throwable = e;
        } finally {
            out.close();
        }
 
    }
}
 
class FastReader {
    BufferedReader bf;
    StringTokenizer tk = null;
 
    public FastReader(BufferedReader bf) {
        this.bf = bf;
    }
 
    public String nextToken () throws Exception {
        if (tk==null || !tk.hasMoreTokens()) {
            tk = new StringTokenizer(bf.readLine());
        }
        if (!tk.hasMoreTokens()) return nextToken();
        else
            return tk.nextToken();
    }
 
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
 
    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
 
    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}