Problem: You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the Ox axis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

<image>

Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

Input

The first line contains three integers w, h, α (1 ≤ w, h ≤ 106; 0 ≤ α ≤ 180). Angle α is given in degrees.

Output

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

1 1 45


Output

0.828427125


Input

6 4 30


Output

19.668384925

Note

The second sample has been drawn on the picture above.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.awt.*;
import java.awt.geom.*;

public class A {

    void solve() throws IOException {
        in("__std"); out("__std");

        double w = readInt();
        double h = readInt();
        double a = readInt();

        AffineTransform transform = new AffineTransform();
        transform.rotate(Math.toRadians(a), 0.5 * w, 0.5 * h);

        Rectangle.Double rectangle = new Rectangle.Double(0, 0, w, h);
        Shape transformed = transform.createTransformedShape(rectangle);

        Area area = new Area(rectangle);
        area.intersect(new Area(transformed));

        java.util.List<Point.Double> points = new ArrayList<Point.Double>();
        PathIterator i = area.getPathIterator(new AffineTransform());
        double[] p = new double[2];
        while (!i.isDone()) {
            i.currentSegment(p);
            points.add(new Point.Double(p[0], p[1]));
            i.next();
        }
        points.add(points.get(0));

        double ans = 0;
        for (int j = 0; j < points.size() - 1; ++j) {
            Point.Double p1 = points.get(j);
            Point.Double p2 = points.get(j + 1);
            ans += p1.y * p2.x - p1.x * p2.y;
        }
        println(0.5 * ans);

        exit();
    }

    void in(String name) throws IOException {
        if (name.equals("__std")) {
            in = new BufferedReader(new InputStreamReader(System.in));
        } else {
            in = new BufferedReader(new FileReader(name));
        }
    }

    void out(String name) throws IOException {
        if (name.equals("__std")) {
            out = new PrintWriter(System.out);
        } else {
            out = new PrintWriter(name);
        }
    }

    void exit() {
        out.close();
        System.exit(0);
    }

    char readChar() throws IOException {
        return (char) in.read();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readToken());
    }

    long readLong() throws IOException {
        return Long.parseLong(readToken());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readToken());
    }

    String readLine() throws IOException {
        st = null;
        return in.readLine();
    }

    String readToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    boolean eof() throws IOException {
        return !in.ready();
    }

    void print(String format, Object ... args) {
        out.print(new Formatter(Locale.US).format(format, args));
    }

    void println(String format, Object ... args) {
        out.println(new Formatter(Locale.US).format(format, args));
    }

    void print(Object value) {
        out.print(value);
    }

    void println(Object value) {
        out.println(value);
    }

    void println() {
        out.println();
    }

    StringTokenizer st;

    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        new A().solve();
    }
}