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.PrintStream;
import java.io.BufferedInputStream;
import java.util.concurrent.Callable;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;

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

	static class TaskO {
		public void solve(int testNumber, BufferedInputStream _in, PrintWriter out) {

			InputReader in = new InputReader(_in);
			long startTime = System.currentTimeMillis();
			int nt = 1;
			Task t = new Task(1);
			t.readInput(in);
			t.call();
			t.writeOutput(out);
			in.close();
			System.err.println("Time: " + (System.currentTimeMillis() - startTime) + " miliseconds");
		}

	}

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

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

		public void close() {
			try {
				if (reader != null)
					reader.close();
			} catch (Exception ex) {
				throw new RuntimeException(ex);
			}
		}

	}

	static class Point implements Comparable<Point> {
		public long x;
		public long y;

		public Point(Point o) {
			this.x = o.x;
			this.y = o.y;

		}

		public Point(long x, long y) {
			super();

			this.x = x;
			this.y = y;
		}


		public int compareTo(Point o2) {
			int t = Long.compare(y, o2.y);
			if (t != 0) return t;
			return Long.compare(x, o2.x);
		}

		public long abs() {
			return (x * x) + (y * y);
		}

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


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


		public int hashCode() {
			return Long.hashCode(x) ^ Long.hashCode(y);
		}

		public boolean equals(Object obj) {
			if (obj instanceof Point) {
				return compareTo((Point) obj) == 0;
			}
			return false;
		}

	}

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

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

		public PointD(long x, long y) {
			this.x = x;
			this.y = y;
		}

		public PointD(PointD o) {
			this.x = o.x;
			this.y = o.y;
		}

		public PointD(Point o) {
			this.x = o.x;
			this.y = o.y;
		}


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


		public String toString() {
			return String.format("%.20f", x) + " " + String.format("%.20f", y);
		}


		public int hashCode() {
			return Double.hashCode(x) ^ Double.hashCode(y);
		}

		public boolean equals(Object obj) {
			if (obj instanceof PointD) {
				return compareTo((PointD) obj) == 0;
			}
			return false;
		}

	}

	static class Task implements Callable<Task> {
		long px;
		long py;
		long vx;
		long vy;
		long a;
		long b;
		long c;
		long d;
		PointD A;
		PointD B;
		PointD C;
		PointD D;
		PointD E;
		PointD F;
		PointD H;
		int testNumber;

		public void readInput(InputReader in) {
	/* read input here */
			px = in.nextLong();
			py = in.nextLong();
			vx = in.nextLong();
			vy = in.nextLong();
			a = in.nextLong();
			b = in.nextLong();
			c = in.nextLong();
			d = in.nextLong();


		}

		public Task call() {
	/* process main algorithm here */

			Point v = new Point(vx, vy);

			double vdx = vx / v.norm();
			double vdy = vy / v.norm();
			A = new PointD(px + vdx * b, py + vdy * b);

			double v2x = -vdy;
			double v2y = vdx;
			B = new PointD(px + v2x * a / 2.0, py + v2y * a / 2.0);
			C = new PointD(px + v2x * c / 2.0, py + v2y * c / 2.0);
			D = new PointD(C.x - vdx * d, C.y - vdy * d);
			F = new PointD(px - v2x * c / 2.0, py - v2y * c / 2.0);
			H = new PointD(px - v2x * a / 2.0, py - v2y * a / 2.0);
			E = new PointD(F.x - vdx * d, F.y - vdy * d);
			System.err.println("Test case: " + testNumber + " done!");
			return this;
		}

		public void writeOutput(PrintWriter out) {

			out.println(A);
			out.println(B);
			out.println(C);
			out.println(D);
			out.println(E);
			out.println(F);
			out.println(H);


		}

		Task(int testNumber) {
			this.testNumber = testNumber;
		}

	}
}