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:

/**
 * Author:-Harsh Chaudhari
 * College:-DA-IICT
 */
import java.util.*;
import java.io.*;

public class B747 {

	public static void main(String[] args) {
		InputReader s = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		/*My code starts here.*/
		int x1 = s.nextInt(),y1 = s.nextInt(),x2 = s.nextInt(),y2 = s.nextInt(),x3 = s.nextInt(),y3 = s.nextInt();
		double midx1 = (x1+x2)/2.0,midy1 = (y1+y2)/2.0,midx2 = (x3+x2)/2.0,midy2 = (y3+y2)/2.0,midx3 = (x1+x3)/2.0,midy3 = (y1+y3)/2.0;
		out.println("3");
		out.println((int)(2*midx1-x3)+" "+(int)(2*midy1-y3));
		out.println((int)(2*midx2-x1)+" "+(int)(2*midy2-y1));
		out.println((int)(2*midx3-x2)+" "+(int)(2*midy3-y2));
		/*My code ends here.*/
		out.close();
	}

	static long PowerMod(long a, long b, long m) {
		long tempo;
		if (b == 0)
			tempo = 1;
		else if (b == 1)
			tempo = a;
		else {
			long temp = PowerMod(a, b / 2, m);
			if (b % 2 == 0)
				tempo = (temp * temp) % m;
			else
				tempo = ((temp * temp) % m) * a % m;
		}
		return tempo;
	}

	static class Node implements Comparable<Node> {
		int num, freq, idx;

		public Node(int u, int v, int idx) {
			this.num = u;
			this.freq = v;
			this.idx = idx;
		}

		public int compareTo(Node n) {
			if (this.freq == n.freq)
				return Integer.compare(this.num, n.num);
			return Integer.compare(-this.freq, -n.freq);
		}
	}

	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}