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.

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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.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {
	static double EPS = 1e-7;
	static class Point implements Comparable<Point> {
		public double x, y;
		public Point(double X, double Y) {x = X; y = Y;}
		public Point(Point a, Point b) {this(b.x - a.x, b.y - a.y);}
		public int compareTo(Point p) {return abs(x - p.x) < EPS ? Double.compare(y, p.y) : Double.compare(x, p.x);}
	}
	static class Clockwise implements Comparator<Point> {
		public int compare(Point a, Point b) {
			return Double.compare(cross(a, b), 0);
		}
	}

	static double cross(Point a, Point b) {return a.x * b.y - a.y * b.x;}
	static double dist(Point a, Point b) {return hypot(a.x - b.x, a.y - b.y);}
	// rotate point around the origin at theta degrees
	static Point rotate(Point p, double theta) {
		double delta = toRadians(theta);
		double angle = atan2(p.y, p.x) + delta;
		double r = hypot(p.x, p.y);
		return new Point(r * cos(angle), r * sin(angle));
	}
	// get intersection between two segments ab, cd
	static Point intersection(Point a, Point b, Point c, Point d) {
		Point ab = new Point(a, b);
		Point cd = new Point(c, d);
		Point ac = new Point(a, c);
		double D = -cross(ab, cd);
		double Ds = cross(cd, ac);
		double Dt = cross(ab, ac);
		if (abs(D) < EPS) { // parallel
			if (abs(Ds) < EPS) { // collinear
				Point[] p = {a, b, c, d};
				Arrays.sort(p);
				return p[1].compareTo(p[2]) == 0 ? p[1] : null;
			}
			return null;
		}
		double s = Ds / D, t = Dt / D;
		if (min(s, t) < -EPS || max(s, t) > 1 + EPS)
			return null;
		return new Point(a.x + s * ab.x, a.y + s * ab.y);
	}
	// get area of polygon
	static double area(List<Point> poly) {
		double a = 0;
		for (int i = 0, j = poly.size() - 1; i < poly.size(); j = i++)
			a += cross(poly.get(i), poly.get(j));
		return abs(a / 2);
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int w = sc.nextInt();
		int h = sc.nextInt();
		int a = sc.nextInt();
		Point[] rect = {
			new Point(w * 0.5, h * 0.5),
			new Point(-w * 0.5, h * 0.5),
			new Point(-w * 0.5, -h * 0.5),
			new Point(w * 0.5, -h * 0.5)
		};
		Point[] rot = new Point[4];
		for (int i = 0; i < 4; ++i)
			rot[i] = rotate(rect[i], a);
		List<Point> poly = new ArrayList<>();
		for (int i = 0; i < 4; ++i) {
			for (int j = 0; j < 4; ++j) {
				Point p = intersection(rect[i], rect[(i + 1) % 4], rot[j], rot[(j + 1) % 4]);
				if (p != null) poly.add(p);
			}
		}
		Collections.sort(poly, new Clockwise());
		System.out.printf("%.10f\n", area(poly));
	}
}