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:
//package main;

import java.io.*;
import java.util.*;
//import java.math.BigInteger;


public class Main {
    boolean[] mark=new boolean[100005];
    public void solve( ) throws Throwable {
        int ax=in.nextInt(), ay=in.nextInt(), bx=in.nextInt(), by=in.nextInt(), cx=in.nextInt(), cy=in.nextInt();
        out.println(3);
        int d1x=bx-(ax-cx); int d1y=by-(ay-cy); out.println(d1x+" "+d1y);
        int d2x=ax-(bx-cx); int d2y=ay-(by-cy); out.println(d2x+" "+d2y);
        int d3x=bx-(cx-ax); int d3y=by-(cy-ay); out.println(d3x+" "+d3y);
    }
    
    int bs(int level, double mi, double tg){
        if(level==1)
            return 1;
        if(tg==mi)
            return level;
        if(tg<mi)
            return bs(level-1, Math.pow(2, level-2), tg);
        else
            return bs(level-1, Math.pow(2, level-2), tg-mi);
            
    }
    
    void sieve(){
        Arrays.fill(mark, false);
        int limit=(int)Math.sqrt(100000)+2;
        mark[0]=mark[1]=true;
        for(int i=4;i<=100000;i+=2){
            mark[i]=true;
        }
        for(int i=3; i<=100000;i+=2){
            if(!mark[i]){
                if(i<=limit){
                    for(int j=i*i;j<=100000;j+=i*2){
                        mark[j]=true;
                    }
                }
            }
        }
    }
//    class car implements Comparable<car>{
//        public int c, v;
//        @Override
//        public int compareTo(car x){
//            return this.c-x.c;
//        }
//    }
    
    
    public void run( ) {
        in = new FastScanner( System.in );
        out = new PrintWriter( new PrintStream( System.out ), true );

        try {
            solve( );
            out.close( );
            System.exit( 0 );
        } catch( Throwable e ) {
            e.printStackTrace( );
            System.exit( -1 ); 
        }
    }


    public void debug( Object...os ) {
        System.err.println( Arrays.deepToString( os ) );
    }

    public static void main( String[ ] args ) {
        ( new Main( ) ).run( );
    }

    private FastScanner in;
    private PrintWriter out;

    private static class FastScanner {
        private int charsRead;
        private int currentRead;
        private byte buffer[ ] = new byte[ 0x1000 ];
        private InputStream reader;

        public FastScanner( InputStream in ) {
            reader = in;
        }

        public int read( ) {
            if ( charsRead == -1 ) {
                throw  new InputMismatchException( );
            }

            if ( currentRead >= charsRead ) {
                currentRead = 0;
                try {
                    charsRead = reader.read( buffer );

                } catch( IOException e ) {
                    throw new InputMismatchException(  );
                }

                if ( charsRead <= 0 ) {
                    return -1;
                }
            }

            return buffer[ currentRead++ ];
        }

        public int nextInt( ) {
            int c = read( );

            while ( isWhitespace( c ) ) {
                c = read( );
            }

            if ( c == -1 ) {
                throw new NullPointerException( );
            } 

            if ( c != '-' && !( c >= '0' && c <= '9' ) ) {
                throw new InputMismatchException( );
            }

            int sign = c == '-' ? -1 : 1;
            if ( sign == -1 ) {
                c = read( );
            }

            if ( c == -1 || !( c >= '0' && c <= '9' ) ) {
                throw new InputMismatchException( );
            }

            int ans = 0;
            while ( !isWhitespace( c )  && c != -1 ) {
                if ( !( c >= '0' && c <= '9' ) ) {
                    throw  new InputMismatchException( );
                }
                int num = c - '0';
                ans = ans * 10 + num;
                c = read( );
            }

            return ans * sign;
        }

        public long nextLong( ) {
            int c = read( );

            while ( isWhitespace( c ) ) {
                c = read( );
            }

            if ( c == -1 ) {
                throw new NullPointerException( );
            }

            if ( c != '-' && !( c >= '0' && c <= '9' ) ) {
                throw new InputMismatchException( );
            }

            int sign = c == '-' ? -1 : 1;
            if ( sign == -1 ) {
                c = read( );
            }

            if ( c == -1 || !( c >= '0' && c <= '9' ) ) {
                throw new InputMismatchException( );
            }

            long ans = 0;
            while ( !isWhitespace( c )  && c != -1 ) {
                if ( !( c >= '0' && c <= '9' ) ) {
                    throw  new InputMismatchException( );
                }
                int num = c - '0';
                ans = ans * 10 + num;
                c = read( );
            }

            return ans * sign;
        }



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

        public String next( ) {
            int c = read( );
            StringBuffer ans = new StringBuffer( );

            while ( isWhitespace( c ) && c != -1 ) {
                c  = read( );
            }

            if ( c == -1 ) {
                return null;
            }

            while ( !isWhitespace( c ) && c != -1 ) {
                ans.appendCodePoint( c );
                c = read( );
            }

            return ans.toString( );

        }

               
        public String nextLine( ) {
            String ans = nextLine0( );

            while ( ans.trim( ).length( ) == 0 ) {
                ans = nextLine0( );
            }

            return ans;
        }
        
        private String nextLine0( ) {
            int c = read( );
            if ( c == -1 ) {
                return null;
            }
            StringBuffer ans = new StringBuffer( );
            while ( c != '\n' && c != '\r' && c != -1 ) {
                ans.appendCodePoint( c );
                c = read( );
            }

            return ans.toString( );

        }


       
        public double nextDouble( ) {
            int c = read( );
            while ( isWhitespace( c ) ) {
                c = read( );
            }

            if ( c == -1 ) {
                throw new NullPointerException( ); 
            }

            if ( c != '.' && c != '-' && !( c >= '0' && c <= '9' ) ) {
                throw new InputMismatchException( );
            }

            int sign = c == '-' ? -1 : 1;
            if ( c == '-' ) {
                c = read( );
            }
            double ans = 0;
            while ( c != -1 && c != '.' && !isWhitespace( c ) ) {
                if ( !( c >= '0' && c <= '9' ) ) {
                    throw new InputMismatchException( );
                }

                int num = c - '0'; 
                ans = ans * 10.0 + num;
                c = read( );
            }

            if ( !isWhitespace( c ) && c != -1 && c != '.' ) {
                throw new InputMismatchException( );
            }

            double pow10 = 1.0;

            if ( c == '.' ) {
                c = read( );
            }

            while ( !isWhitespace( c ) && c != -1 ) {
                pow10 *= 10.0;

                if ( !( c >= '0' && c <= '9' ) ) {
                    throw new InputMismatchException( );
                }
                int num = c - '0';
                ans = ans * 10.0 + num; 
                c = read( );
            }

            return ans * sign / pow10;
        }
    }

}