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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Objects;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        OArrow solver = new OArrow();
        solver.solve(1, in, out);
        out.close();
    }

    static class OArrow {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            double px = in.nextInt();
            double py = in.nextInt();
            PointF o = new PointF(px, py);
            double vx = in.nextInt();
            double vy = in.nextInt();
            PointF v = new PointF(vy, -vx);
            double a = in.nextInt();
            double b = in.nextInt();
            double c = in.nextInt();
            double d = in.nextInt();

            List<PointF> points = new ArrayList<>();
            points.add(new PointF(0, b));
            points.add(new PointF(-a / 2, 0));
            points.add(new PointF(-c / 2, 0));
            points.add(new PointF(-c / 2, -d));
            points.add(new PointF(c / 2, -d));
            points.add(new PointF(c / 2, 0));
            points.add(new PointF(a / 2, 0));

            for (PointF p : points) {
                p.mult(v);
                p.div(v.len());
                p.add(o);

                out.println(Util.join(Util.formatDouble(p.x), Util.formatDouble(p.y)));
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static class PointF implements Comparable<PointF> {
        public double x;
        public double y;

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

        public double norm() {
            return x * x + y * y;
        }

        public double len() {
            return Math.sqrt(norm());
        }

        public PointF add(PointF o) {
            x += o.x;
            y += o.y;
            return this;
        }

        public PointF mult(PointF o) {
            double newX = x * o.x - y * o.y;
            double newY = x * o.y + y * o.x;
            x = newX;
            y = newY;
            return this;
        }

        public PointF div(double c) {
            x /= c;
            y /= c;
            return this;
        }

        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            PointF point = (PointF) o;
            return x == point.x && y == point.y;
        }

        public int hashCode() {
            return Objects.hash(x, y);
        }

        public int compareTo(PointF o) {
            int ret = Double.compare(x, o.x);
            if (ret != 0)
                return ret;
            return Double.compare(y, o.y);
        }

        public String toString() {
            return String.format("(%f, %f)", x, y);
        }

    }

    static class Util {
        public static String formatDouble(double x) {
            return String.format("%.15f", x);
        }

        public static String join(String... i) {
            StringBuilder sb = new StringBuilder();
            for (Object o : i) {
                sb.append(o);
                sb.append(" ");
            }
            if (sb.length() > 0) {
                sb.deleteCharAt(sb.length() - 1);
            }
            return sb.toString();
        }

    }
}