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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class TaskO {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            Point p = Point.readPoint(in);
            double vx = in.readInt();
            double vy = in.readInt();
            double h = Math.hypot(vx, vy);
            vx /= h;
            vy /= h;
            Vector vector = new Vector(vx, vy);
            Vector other = new Vector(vy, -vx);
            int a = in.readInt();
            int b = in.readInt();
            int c = in.readInt();
            int d = in.readInt();
            p = go(p, vector, b);
            out.printLine(p.x, p.y);
            p = go(p, vector, -b);
            p = go(p, other, -a / 2d);
            out.printLine(p.x, p.y);
            p = go(p, other, -(c - a) / 2d);
            out.printLine(p.x, p.y);
            p = go(p, vector, -d);
            out.printLine(p.x, p.y);
            p = go(p, other, c);
            out.printLine(p.x, p.y);
            p = go(p, vector, d);
            out.printLine(p.x, p.y);
            p = go(p, other, -(c - a) / 2d);
            out.printLine(p.x, p.y);
        }

        private Point go(Point p, Vector vector, double times) {
            return new Point(p.x + vector.x * times, p.y + vector.y * times);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class Vector {
        public final double x;
        public final double y;
        public final Point point;

        public Vector(double x, double y) {
            this.x = x;
            this.y = y;
            point = new Point(x, y);
        }

        public Vector(Point point) {
            this.x = point.x;
            this.y = point.y;
            this.point = point;
        }

        public Vector(Point from, Point to) {
            this(to.x - from.x, to.y - from.y);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        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 readInt() {
            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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class GeometryUtils {
        public static double epsilon = 1e-8;

    }

    static class Point {
        public final double x;
        public final double y;


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

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


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

            Point point = (Point) o;

            return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
        }


        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }

        public static Point readPoint(InputReader in) {
            double x = in.readDouble();
            double y = in.readDouble();
            return new Point(x, y);
        }

    }
}