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.*;
    public class leaderboard {
    public static void main(String[] args) {
    	InputReader s=new InputReader(System.in);
    	int ax=s.nextInt(),ay=s.nextInt(),bx=s.nextInt(),by=s.nextInt(),cx=s.nextInt(),cy=s.nextInt();
        double ab=Math.sqrt((bx-ax)*(bx-ax)+(by-ay)*(by-ay));
        double bc=Math.sqrt((cy-by)*(cy-by)+(cx-bx)*(cx-bx));
        double ac=Math.sqrt((ax-cx)*(ax-cx)+(ay-cy)*(ay-cy));
        System.out.println(3);
        if(ab>bc && ac>bc){
            System.out.println((ax+bx-cx)+" "+(ay+by-cy));
            System.out.println((ax+cx-bx)+" "+(ay+cy-by));
    System.out.println((bx+cx-ax)+" "+(by+cy-ay));
        }
        else if(bc>ab && ac>ab){
            System.out.println((cx-ax+bx)+" "+(cy-ay+by));
            System.out.println((cx+ax-bx)+" "+(cy+ay-by));
            System.out.println((ax+bx-cx)+" "+(ay+by-cy));
        }
        else{
            System.out.println((bx+ax-cx)+" "+(by+ay-cy));
            System.out.println((bx-ax+cx)+" "+(by-ay+cy));
            System.out.println((ax+cx-bx)+" "+(ay+cy-by));
        }
      

        }

        public static boolean isPrime(long n) {
          if(n<=1)
            return false;
          if(n > 2 && (n & 1) == 0)
           return false;
         for(int i = 3; i * i <= n; i += 2)
            if (n % i == 0) 
                return false;
        return true;
    }

        private static long gcd(long number1, long number2) { 
        if(number2 == 0){ 
        return number1;
        }

        return gcd(number2, number1%number2);
        }

        private static long lcm(long a, long b)
        {
         return a * (b / gcd(a, b));
        }

        static long power(long x, long y)
        {
            if( y == 0)
            return 1;
            else if (y%2 == 0)
            return power(x, y/2)*power(x, y/2);
            else
            return x*power(x, y/2)*power(x, y/2); 
        }   





    	static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
     
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
     
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 String nextToken() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }
     
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    }