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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class C {
	
	static class point{
		double x,y;
		public point(double xx,double yy){
			x=xx;
			y=yy;
		}
		public point sub(point a){
			return new point(x - a.x,y - a.y);
		}
		public point add(point a){
			return new point(x + a.x,y + a.y);
		}
		public double cross(point a){
			return x*a.y - y*a.x;
		}
		public point multbyscalar(double ua) {
			return  new point(ua*x,ua*y);
		}
		point rotate(double angle){
			//radianes
			double nx = x * Math.cos(angle) - Math.sin(angle) * y;
			double ny = x * Math.sin(angle) + Math.cos(angle) * y;
			return new point(nx,ny);
		}
	}
	
	static double eps=1e-8;
	
	static point intersectionbtwlines(point p1,point p2,point p3,point p4){
		point p2_p1=p2.sub(p1);
		point p4_p3=p4.sub(p3);
		double den=p2_p1.cross(p4_p3);
		if (Math.abs(den)<eps)//the lines are parallel or coincident
			return null;
		point p1_p3=p1.sub(p3);
		double num=p4_p3.cross(p1_p3);
		double ua=num/den;
		return p2_p1.multbyscalar(ua).add(p1);
	}
	
	static point[] sutherland_hodgman(point[]  line,point[] poly,int flag){
		ArrayList<point> output=new ArrayList<point>();
		point S=poly[poly.length-1];
		for(int i=0;i<poly.length;i++){
			point E=poly[i];
			double ecross=line[1].sub(line[0]).cross(E.sub(line[0]));
			double scross=line[1].sub(line[0]).cross(S.sub(line[0]));
			if (Math.abs(ecross)<eps)
				output.add(E);
			else if (ecross*flag>eps){
				if (scross*flag<-eps)
					output.add(intersectionbtwlines(line[0],line[1],S,E));
				output.add(E);
			}
			else if(scross*flag>eps)
				output.add(intersectionbtwlines(line[0],line[1],S,E));
			S=E;
		}
		point[] ret=new point[output.size()];
		return output.toArray(ret);
	}
	
	static point[] getpoly(point[] line, point[] poly){
		return sutherland_hodgman(line,poly,1);
	}
	
	static double polygonarea(point[] a, int n){
		double r=0;
		for(int i=0;i<n;i++)
			r+=a[i].cross(a[(i+1)%n]);
		return Math.abs(r/2.0);
	}
	
	static point[] initpoly(int W, int H){
		point[] ret=new point[4];
		ret[0]=new point(-W/2.0,-H/2.0);
		ret[1]=new point(W/2.0,-H/2.0);
		ret[2]=new point(W/2.0,H/2.0);
		ret[3]=new point(-W/2.0,H/2.0);
		return ret;
	}
	
	static class Scanner{
		BufferedReader br=null;
		StringTokenizer tk=null;
		public Scanner(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		public String next() throws IOException{
			while(tk==null || !tk.hasMoreTokens())
				tk=new StringTokenizer(br.readLine());
			return tk.nextToken();
		}
		public int nextInt() throws NumberFormatException, IOException{
			return Integer.valueOf(next());
		}
		public double nextDouble() throws NumberFormatException, IOException{
			return Double.valueOf(next());
		}
	}
	
	static int W,H,alpha;
	
	public static void main(String args[]) throws NumberFormatException, IOException{
		Scanner sc = new Scanner();
		int W = sc.nextInt();
		int H = sc.nextInt();
		int alpha = sc.nextInt();
		point[] fixed = initpoly(W,H);
		point[] rotated = initpoly(W,H);
		double angle = (alpha / 180.0) * Math.PI;
		for(int i = 0 ; i < 4 ; i++)
			rotated[i] =rotated[i].rotate(angle);
		for(int i = 0; i < 4; i++){
			point[] line={rotated[i],rotated[(i + 1) % 4]};
			fixed = getpoly(line,fixed);
		}
		System.out.println(polygonarea(fixed,fixed.length));
	}

}