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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.io.BufferedInputStream;
import java.util.concurrent.Callable;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		BufferedInputStream in = new BufferedInputStream(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskB {
		public void solve(int testNumber, BufferedInputStream _in, PrintWriter out) {

			InputReader in = new InputReader(_in);
			long startTime = System.currentTimeMillis();
			int nt = 1;
			Task t = new Task(1);
			t.readInput(in);
			t.call();
			t.writeOutput(out);
			in.close();
			System.err.println("Time: " + (System.currentTimeMillis() - startTime) + " miliseconds");
		}

	}

	static class Task implements Callable<Task> {
		ArrayList<Point> lp = new ArrayList<>();
		HashSet<Point> re = new HashSet<>();
		int testNumber;

		public void readInput(InputReader in) {
	/* read input here */
			lp.add(new Point(in.nextInt(), in.nextInt()));
			lp.add(new Point(in.nextInt(), in.nextInt()));
			lp.add(new Point(in.nextInt(), in.nextInt()));
		}

		public Task call() {
	/* process main algorithm here */
			for (int i = 0; i < lp.size(); ++i)
				for (int j = 0; j < lp.size(); ++j)
					if (i != j) {
						Point v = lp.get(i).opSub(lp.get(j));
						Point p = null;
						for (int k = 0; k < lp.size(); ++k)
							if (k != i && k != j) {
								p = lp.get(k);
								break;
							}

						re.add(v.opPlus(p));
						//re.add(v.opSub(p));
					}

			System.err.println("Test case: " + testNumber + " done!");
			return this;
		}

		public void writeOutput(PrintWriter out) {
			out.println(re.size());
			for (Point p : re) out.println(p);

		}

		Task(int testNumber) {
			this.testNumber = testNumber;
		}

	}

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

		public void close() {

		}

	}

	static class Point implements Comparable<Point> {
		public long x;
		public long y;

		public Point(Point o) {
			this.x = o.x;
			this.y = o.y;

		}

		public Point(long x, long y) {
			super();

			this.x = x;
			this.y = y;
		}


		public int compareTo(Point o2) {
			int t = Long.compare(y, o2.y);
			if (t != 0) return t;
			return Long.compare(x, o2.x);
		}

		public Point opSub(Point b) {
			return Point._opSub(this, b);
		}

		public Point opPlus(Point b) {
			return Point._opPlus(this, b);
		}

		public static Point _opSub(Point lhs, Point rhs) {
			return new Point((lhs.x - rhs.x), (lhs.y - rhs.y));
		}

		public static Point _opPlus(Point lhs, Point rhs) {
			return new Point((lhs.x + rhs.x), (lhs.y + rhs.y));
		}


		public String toString() {
			return x + " " + y;
		}


		public int hashCode() {
			return Long.hashCode(x) ^ Long.hashCode(y);
		}

		public boolean equals(Object obj) {
			if (obj instanceof Point) {
				return compareTo((Point) obj) == 0;
			}
			return false;
		}

	}
}