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.io.*;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

/**
 * Created by twist.ma on 16/12/16.
 */
public class Main {

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
//        Tester.solve(in, out);
        solve(in, out);
        out.close();
    }

    public static void solve(InputReader in,OutputWriter out) {
        Node n1 = new Node(in.readInt(),in.readInt());
        Node n2 = new Node(in.readInt(),in.readInt());
        Node n3 = new Node(in.readInt(),in.readInt());

        Vector v12 = new Vector(n1.x - n2.x, n1.y - n2.y);
        Vector v23 = new Vector(n2.x - n3.x, n2.y - n3.y);

        Set<Node> nodes = new HashSet<>();
        nodes.add(n3.plusVector(v12));
        nodes.add(n3.subVector(v12));
        nodes.add(n1.plusVector(v23));
        nodes.add(n1.subVector(v23));

        out.printLine(nodes.size());
        for (Node node : nodes) {
            out.printLine(node.x + " " + node.y);
        }
    }

}

class Node{
    int x,y;

    public Node(int x, int y) {
        this.x = x;
        this.y = y;
    }


    public Node plusVector(Vector v) {
        Node newNode = new Node(x,y);
        newNode.x += v.x;
        newNode.y += v.y;
        return newNode;
    }


    public Node subVector(Vector v) {
        Node newNode = new Node(x,y);
        newNode.x -= v.x;
        newNode.y -= v.y;
        return newNode;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Node node = (Node) o;

        return x == node.x && y == node.y;

    }

    @Override
    public int hashCode() {
        int result = x;
        result = 31 * result + y;
        return result;
    }
}

class Vector{
    int x,y;

    public Vector(int x, int y) {
        this.x = x;
        this.y = y;
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

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

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

    public String readLine() {
        StringBuilder sb = new StringBuilder();
        int c;
        while ((c = read()) != -1 & !isEndLine(c)) {
            sb.append(c);
        }
        return sb.toString();
    }

    public int readInt() {
        int c = read();
        while (isWhitespace(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 (!isWhitespace(c));
        return res * sgn;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' ;
    }

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

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

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void close() {
        writer.close();
    }

    public void printLine(long i) {
        writer.println(i);
        writer.flush();
    }

    public void printLine(String i) {
        writer.println(i);
        writer.flush();
    }

    public void printWithSpace(long i) {
        writer.print(i);
        writer.print(" ");
        writer.flush();
    }

    public void print(long i) {
        writer.print(i);
        writer.flush();
    }

    public void print(String i) {
        writer.print(i);
        writer.flush();
    }

}

class Tester{
    public static long time = 0;
    public static long size = 0;

    public static void solve(InputReader in,OutputWriter out) {
        time = System.currentTimeMillis();
        Runtime runtime = Runtime.getRuntime();
        size = runtime.totalMemory() - runtime.freeMemory();
        Main.solve(in,out);
        System.out.println("耗时:" + (System.currentTimeMillis() - time));
        System.out.println("内存:" + (runtime.totalMemory() - runtime.freeMemory() - size));
    }
}