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

public class Main {

	void solve() {
		double w = sc.nextDouble();
		double h = sc.nextDouble();
		double a = sc.nextDouble();
		if (a >= 90) { a = 180 - a; }
		a = a / 180 * Math.PI;


		P[] ps = new P[4];
		ps[0] = new P(w/2,h/2);
		ps[1] = new P(-w/2,h/2);
		ps[2] = new P(-w/2,-h/2);
		ps[3] = new P(w/2,-h/2);

		P[] ps2 = new P[4];
		for (int i = 0; i < 4; i++) {
			ps2[i] = ps[i].mul(new P(cos(a), sin(a)));
		}

		for (int i = 0; i < 4; i++) {
			ps = convexCut(ps, ps2[i], ps2[(i+1)&3]);
		}
		out.printf("%.9f\n", area(ps));
	}


	final double EPS = 1e-10;

	class P implements Comparable<P> {
		double x, y;
		public P(double x, double y) {
			this.x = x;
			this.y = y;
		}
		public int compareTo(P o) {
			return x != o.x ? Double.compare(x, o.x) : Double.compare(y, o.y);
		}
		public String toString() {
			return "(" + x + "," + y + ")";
		}
		public double abs() {return sqrt(x * x + y * y); }
		public double abs2() {return x * x + y * y; }
		public double arg() { return atan2(y, x); }
		public P mul(double k) {return new P(x * k, y * k);}
		public P div(double k) {return new P(x / k, y / k);}
		public P add(P o) {return new P(x + o.x, y + o.y);}
		public P sub(P o) {return new P(x - o.x, y - o.y);}
		public P mul(P o) {return new P(x * o.x - y * o.y,  x * o.y + y * o.x); }
		public P div(P o) {return new P(x * o.x + y * o.y, -x * o.y + y * o.x).div(o.abs2()); }
		public double dot(P o) {return x * o.x + y * o.y;} // a b sin(t)
		public double det(P o) {return x * o.y - y * o.x;} // a b cos(t)
		public P normal() { return this.div(this.abs()); }
		public P rot90() { return new P(-y, x); }
	}

	int ccw(P a, P b, P c) {
		double cross = (b.sub(a)).det(c.sub(a));
		if (cross > EPS) return +1;
		if (cross < EPS) return -1;
		return 0;
	}
	boolean isIntersectLL(P a,P b,P c,P d){
		return abs(b.sub(a).det(d.sub(c))) > EPS || // non-parallelabs
		(b.sub(a).det(c.sub(a))) < EPS; // same line
	}
	boolean isIntersectSS(P a1, P a2, P b1, P b2) {
		return ccw(a1, a2, b1) * ccw(a1, a2, b2) <= 0 && ccw(b1, b2, a1) * ccw(b1, b2, a2) <= 0;
	}
	double distanceLP(P p1, P p2, P q) {
		return abs(p2.sub(p1).det(q.sub(p1))) / p2.sub(p1).abs();
	}
	P intersectionLL(P a1, P a2, P b1, P b2) {
		P a = a2.sub(a1);
		P b = b2.sub(b1);
		return a1.add(a.mul(b.det(b1.sub(a1))).div(b.det(a)));
	}
	P[] convexHull(P[] ps) {
		int n = ps.length;
		int k = 0;
		if (n <= 1) return ps;
		sort(ps);
		P[] qs = new P[n * 2];
		for (int i = 0; i < n; qs[k++] = ps[i++]) {
			while (k > 1 && qs[k-1].sub(qs[k-2]).det(ps[i].sub(qs[k-1])) < EPS) k--;
		}
		for (int i = n-2, t = k; i >= 0; qs[k++] = ps[i--]) {
			while (k > t && qs[k-1].sub(qs[k-2]).det(ps[i].sub(qs[k-1])) < EPS) k--;
		}
		P[] res = new P[k-1];
		System.arraycopy(qs, 0, res, 0, k-1);
		return res;
	}
	// 凸多角形をある直線で切断し、左側を残す。
	// 凸多角形は半時計回りに与えられていること
	P[] convexCut(P[] poly, P p1, P p2) {
	  int N = poly.length;
	  P[] ret = new P[N + 2];
	  int rs = 0;
	  for (int i = 0; i < N; i++) {
	      P a = poly[i];
	      P b = poly[(i+1)%N];
	      if( ccw(p1, p2, a) != -1 ) ret[rs++] = a;
	      if( ccw(p1, p2, a) * ccw(p1, p2, b) == -1 )
	          ret[rs++] = intersectionLL(a,b,p1,p2);
	  }
	  return copyOf(ret, rs);
	}
	double area(P[] v){
		  double ret = 0.0;
		  int SZ = v.length;
		  for(int i=0; i < SZ; i++){
		    ret += v[i].det(v[(i+1) % SZ]);
		  }
		  ret = abs(ret / 2.0);
		  return ret;
		}


	public static void main(String[] args) throws Exception {
		Class<?> here = new Object(){}.getClass().getEnclosingClass();
		try {
			String packageName = here.getPackage().getName();
			packageName = "src/" + packageName.replaceAll("\\.", "/") + "/";
			System.setIn(new FileInputStream(packageName + "input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream(packageName + "output.txt")));
		} catch (FileNotFoundException e) {
		} catch (NullPointerException e) {
		}

		Object o = Class.forName(here.getName()).newInstance();
		o.getClass().getMethod("run").invoke(o);
	}

	static void tr(Object... os) {
		System.err.println(deepToString(os));
	}


	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	void print(int[] a) {
		out.print(a[0]);
		for (int i = 1; i < a.length; i++) out.print(" " + a[i]);
		out.println();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}

		public String next() {
			eat();
			return tokenizer.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}