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:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Andy Phan
 */
public class o {

    public static void main(String[] args) {
        FS in = new FS(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
        Vec p = new Vec(in.nextInt(), in.nextInt());
        Vec v = new Vec(in.nextInt(), in.nextInt());
        v = v.unit();
        Vec vr = v.rot270();
        
        double a = in.nextInt();
        double b = in.nextInt();
        double c = in.nextInt();
        double d = in.nextInt();
        
        System.out.println(p.add(v.scale(b)));
        System.out.println(p.add(vr.scale(-a/2)));
        System.out.println(p.add(vr.scale(-c/2)));
        System.out.println(p.add(vr.scale(-c/2)).add(v.scale(-d)));
        System.out.println(p.add(vr.scale(c/2)).add(v.scale(-d)));
        System.out.println(p.add(vr.scale(c/2)));
        System.out.println(p.add(vr.scale(a/2)));

        out.close();
    }

    static class Vec {

        static final double EPS = 1e-6;
        double x, y;

        public Vec(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public Vec add(Vec o) {
            return new Vec(x + o.x, y + o.y);
        }

        public Vec sub(Vec o) {
            return new Vec(x - o.x, y - o.y);
        }

        public Vec scale(double s) {
            return new Vec(x * s, y * s);
        }

        public double dot(Vec o) {
            return x * o.x + y * o.y;
        }

        public double cross(Vec o) {
            return x * o.y - y * o.x;
        }

        public double mag2() {
            return dot(this);
        }

        public double mag() {
            return Math.sqrt(mag2());
        }

        public Vec unit() {
            return scale(1 / mag());
        }

        public Vec rot90() {
            return new Vec(-y, x);
        }

        public Vec rot270() {
            return new Vec(y, -x);
        }

        public Vec rotate(double theta) {
            double PI = Math.PI;
            double newX = x * Math.cos(theta) + y * Math.cos(PI / 2 + theta);
            double newY = x * Math.sin(theta) + y * Math.sin(PI / 2 + theta);
            return new Vec(newX, newY);
        }

        //angle between 0 and 2PI
        public double angle() {
            return (Math.atan2(y, x) + 2 * Math.PI) % (2 * Math.PI);
        }

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

        static boolean eq(double a, double b) {
            return Math.abs(a - b) < EPS;
        }

        static boolean leq(double a, double b) {
            return a - EPS < b;
        }

        static boolean geq(double a, double b) {
            return a + EPS > b;
        }

        public boolean equals(Object oo) {
            Vec o = (Vec) oo;
            return eq(x, o.x) && eq(y, o.y);
        }
    }

    static class FS {

        BufferedReader in;
        StringTokenizer token;

        public FS(InputStream str) {
            in = new BufferedReader(new InputStreamReader(str));
        }

        public String next() {
            if (token == null || !token.hasMoreElements()) {
                try {
                    token = new StringTokenizer(in.readLine());
                } catch (IOException ex) {
                }
                return next();
            }
            return token.nextToken();
        }

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