Problem: Petya has recently started working as a programmer in the IT city company that develops computer games.

Besides game mechanics implementation to create a game it is necessary to create tool programs that can be used by game designers to create game levels. Petya's first assignment is to create a tool that allows to paint different arrows on the screen.

A user of this tool will choose a point on the screen, specify a vector (the arrow direction) and vary several parameters to get the required graphical effect. In the first version of the program Petya decided to limit parameters of the arrow by the following: a point with coordinates (px, py), a nonzero vector with coordinates (vx, vy), positive scalars a, b, c, d, a > c.

The produced arrow should have the following properties. The arrow consists of a triangle and a rectangle. The triangle is isosceles with base of length a and altitude of length b perpendicular to the base. The rectangle sides lengths are c and d. Point (px, py) is situated in the middle of the triangle base and in the middle of side of rectangle that has length c. Area of intersection of the triangle and the rectangle is zero. The direction from (px, py) point to the triangle vertex opposite to base containing the point coincides with direction of (vx, vy) vector.

Enumerate the arrow points coordinates in counter-clockwise order starting from the tip.

<image>

Input

The only line of the input contains eight integers px, py, vx, vy ( - 1000 ≤ px, py, vx, vy ≤ 1000, vx2 + vy2 > 0), a, b, c, d (1 ≤ a, b, c, d ≤ 1000, a > c).

Output

Output coordinates of the arrow points in counter-clockwise order. Each line should contain two coordinates, first x, then y. Relative or absolute error should not be greater than 10 - 9.

Examples

Input

8 8 0 2 8 3 4 5


Output

8.000000000000 11.000000000000
4.000000000000 8.000000000000
6.000000000000 8.000000000000
6.000000000000 3.000000000000
10.000000000000 3.000000000000
10.000000000000 8.000000000000
12.000000000000 8.000000000000

Solution (in JAVA):

Solution:
/**
 * Created by mo on 3/2/17.
 */

import java.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Arrow {
    static StringBuilder sb;

    /**
     * Because we treat vertical as no rotation, subtract angle by PI/2 to account for this.
     */
    public static void main(String[] args) {
        //Scanner sc = new Scanner(System.in);
        FastScanner sc = new FastScanner();
        boolean debug = false;
        double px = sc.nextDouble(), py = sc.nextDouble(); //Points of origin
        double vx = sc.nextDouble(), vy = sc.nextDouble(); //Vector from origin
        double a = sc.nextDouble(); //Base of isosceles triangle
        double b = sc.nextDouble(); //Height of isosceles triangle
        double c = sc.nextDouble(); //Base of rectangle
        double d = sc.nextDouble(); //Height of rectangle
        
        Point[] points = new Point[7];

        double theta = atan2(vy, vx) - (PI / 2); //this subtraction is key

        if (debug) System.out.println("theta is " + theta);

        /**
         * Order the points counterclockwise, treating (px, py) as origin
         */
        points[0] = new Point(0, 1 * b);
        points[1] = new Point(-a/2, 0);
        points[2] = new Point(-c/2, 0);
        points[3] = new Point(-c/2, -1 * d);
        points[4] = new Point(c/2, -1 * d);
        points[5] = new Point(c/2, 0);
        points[6] = new Point(a/2, 0);


        for (int i = 0; i < 7; i++) {
            //Rotate about theta, and then slide into place.
            Point p = points[i].rotate(theta).slide(px, py);
            System.out.println(p.x + " " + p.y);
        }
    }

    public static double mag(Point p) {
        return sqrt(p.x * p.x + p.y * p.y);
    }

    static class Point {
        double x, y;
        
        Point (double _x, double _y) {
            this.x = _x;
            this.y = _y;
        }

        Point rotate (double theta) {
            //Convert to polar, rotate, convert back
            double r = mag(this);
            double theta1 = atan2(this.y, this.x);
            double thetaSum = theta1 + theta;
            return new Point(cos(thetaSum) * r, sin(thetaSum) * r);
        }

        Point slide (double dx, double dy) {
            //Simple translate function
            return new Point(this.x + dx, this.y + dy);
        }
    }



    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextLong();
            }
            return a;
        }
    }
}