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.InputStreamReader;
import static java.lang.Math.*;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Scanner;
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author pttrung
 */
public class C {

    public static void main(String[] args) {
        Scanner in = new Scanner(new InputStreamReader(System.in));
        int w = in.nextInt();
        int h = in.nextInt();
        int c = in.nextInt();
        c = Math.min(c, 180 - c);
        if (c == 0) {
            double result = (double) w * h;
            System.out.println(result);
        } else if (c == 90) {
            double result = (double) w * w;
            System.out.println(result);
        } else {
            double angle = (double) c * PI / 180;
            Point[] rec = new Point[4];
            rec[0] = new Point((double) w / 2, (double) h / 2);
            rec[1] = new Point((double) -w / 2, (double) h / 2);
            rec[2] = new Point((double) -w / 2, (double) -h / 2);
            rec[3] = new Point((double) w / 2, (double) -h / 2);

            Point[] other = new Point[4];
            for (int i = 0; i < 4; i++) {
                other[i] = convert(rec[i], angle);
                //  System.out.println(other[i]);
            }
            ArrayList<Point> p = new ArrayList();
            for (int i = 0; i < 4; i++) {
                int j = (i + 1) % 4;
                check(other[i], other[j], p, rec, i);
            }
            double result = 0;
            for (int i = 0; i < p.size(); i++) {
                int j = (i + 1) % p.size();
                //  System.out.println(p.get(i));
                result += Math.abs(cross(p.get(i), p.get(j)));
            }

            System.out.println(result / 2);
        }
    }

    static void check(Point a, Point b, ArrayList<Point> p, Point[] rec, int index) {
        for (int i = 0; i < 4; i++) {
            int m = (i + index) % 4;
            int j = (i + 1 + index) % 4;
            Point k = intersect(minus(b, a), minus(rec[m], rec[j]), minus(rec[m], a));
            if (k.x >= 0 && k.x <= 1 && k.y >= 0 && k.y <= 1) {
                Point val = new Point(k.x * minus(b, a).x, k.x * minus(b, a).y);
                p.add(add(val, a));
                // System.out.println(a + " " + b + " " + rec[i] + " " + rec[j]);
                // System.out.println(add(val, a));
            }
        }
    }

    static Point intersect(Point a, Point b, Point c) {
        double D = cross(a, b);
        if (D != 0) {
            return new Point(cross(c, b) / D, cross(a, c) / D);
        }
        return null;
    }

    static Point convert(Point a, double angle) {
        double x = a.x * cos(angle) - a.y * sin(angle);
        double y = a.x * sin(angle) + a.y * cos(angle);
        return new Point(x, y);
    }

    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static Point add(Point a, Point b) {
        return new Point(a.x + b.x, a.y + b.y);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    static class Point {

        double x, y;

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

        @Override
        public String toString() {
            return "Point: " + x + " " + y;
        }
    }
}