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.lang.*;
import java.awt.geom.*;
import java.io.*;
import java.math.*;
import java.util.*;

public class T280A implements Runnable {
    
    double getX(double x, double y, double alpha) {
        return Math.cos(alpha*Math.PI/180)*x+Math.sin(alpha*Math.PI/180)*y;
    }
    double getY(double x, double y, double alpha) {
        return -Math.sin(alpha*Math.PI/180)*x+Math.cos(alpha*Math.PI/180)*y;
    }
    
    private class P implements Comparable<P> {
        double x, y;
        
        public P(double x, double y) {
            this.x = x; this.y = y;
        }
        
        public int compareTo(P a) {
            return (int)(Math.signum(x*a.y - y*a.x));
        }
    }
    
    public void run() {
        double w = nextDouble();
        double h = nextDouble();
        double alpha = nextDouble();
        
        double[] x1 = {-w/2.0, -w/2.0, w/2.0, w/2.0};
        double[] y1 = {h/2.0, -h/2.0, -h/2.0, h/2.0};
        
        double[] x2 = new double[4];
        double[] y2 = new double[4];
        for (int i = 0; i < 4; ++i) {
            x2[i] = getX(x1[i], y1[i], alpha);
            y2[i] = getY(x1[i], y1[i], alpha);
        }
        
        List<P> pts = new ArrayList<P>();
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 4; ++j) {
                if (Line2D.linesIntersect(x1[i], y1[i], x1[(i+1)%4], y1[(i+1)%4],
                        x2[j], y2[j], x2[(j+1)%4], y2[(j+1)%4])) {
                    double A1 = y1[(i+1)%4] - y1[i];
                    double B1 = x1[i] - x1[(i+1)%4];
                    double C1 = -(A1*x1[(i+1)%4] + B1*y1[(i+1)%4]);
                    double A2 = y2[(j+1)%4] - y2[j];
                    double B2 = x2[j] - x2[(j+1)%4];
                    double C2 = -(A2*x2[(j+1)%4] + B2*y2[(j+1)%4]);
                    
                    double D = A1*B2 - A2*B1;
                    if (Math.abs(D) > 1e-11) {
                        double X = (C1*B2 - C2*B1)/D;
                        double Y = (A1*C2 - A2*C1)/D;
                        pts.add(new P(X, Y));
                    }
                }
            }
        }
        
        Collections.sort(pts);
        
        double res = 0;
        for (int i = 0; i < pts.size(); ++i) {
            P p1 = pts.get(i);
            P p2 = pts.get((i+1)%pts.size());
            res += Math.abs(p1.x*p2.y - p2.x*p1.y)/2.0;
        }
        out.printf(Locale.ENGLISH, "%.8f\n", res);
        out.flush();
    }
    
    private static BufferedReader br = null;
    private static PrintWriter out = null;
    private static StringTokenizer stk = null;
    
    public static void main(String[] args) throws IOException{
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        (new T280A()).run();
    }
    
    private void loadLine() {
        try {
            stk = new StringTokenizer(br.readLine());
        }
        catch (IOException e) {
            e.printStackTrace();
        }
    }
    
    private String nextLine() {
        try {
            return (br.readLine());
        }
        catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }
    
    private int nextInt() {
        while (stk == null || !stk.hasMoreElements()) loadLine();
        return Integer.parseInt(stk.nextToken());
    }
    
    private long nextLong() {
        while (stk == null || !stk.hasMoreElements()) loadLine();
        return Long.parseLong(stk.nextToken());
    }
    
    private double nextDouble() {
        while (stk == null || !stk.hasMoreElements()) loadLine();
        return Double.parseDouble(stk.nextToken());
    }
    
    private String nextWord() {
        while (stk == null || !stk.hasMoreElements()) loadLine();
        return (stk.nextToken());
    }
    
}