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.math.BigInteger.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

public class A {

	final static boolean autoflush = false;
	
	public A () {
		int L = sc.nextInt();
		int M = sc.nextInt();
		int Z = sc.nextInt();
		
		double W = max(L, M);
		double H = min(L, M);
		
		if (Z == 0 || Z == 180)
			exit(W*H);
		
		if (Z == 90)
			exit(H*H);
		
		if (Z > 90)
			Z = 180 - Z;
		
		double G = Z * PI / 180;
		
		double C = cos(G), S = sin(G); W /= 2; H /= 2;

		Double [] P = { W*C - H*S, W*S + H*C }; 
		Double [] Q = { W*C + H*S, W*S - H*C };
		double D = (Q[1] - P[1]) / (Q[0] - P[0]);
		
		Double [] X = { P[0] + (H - P[1]) / D, H };
		Double [] Y = { W, P[1] + (W - P[0]) * D }; 

		double A, B = 0;
		double a, b = 0;
		
		a = dist(P, X);
		if (X[0] > Q[0])
			b = dist(X, Q);
		A = (a*a - b*b) / tan(G);
		
		if (Y[0] < Q[0]) {
			a = dist(Y, Q);
			B = a*a * tan(G);
		}
		
		double res = 4*W*H - A - B;
		exit(res);
	}

	double norm (Double ...X) {
		double res = 0;
		for (double x : X)
			res += x*x;
		return sqrt(res);
	}
	
	double dist(Double [] X, Double [] Y) {
		int N = X.length;
		Double [] Z = new Double [N];
		for (int i : rep(N))
			Z[i] = X[i] - Y[i];
		double res = norm(Z);
		return res;
	}
	
	////////////////////////////////////////////////////////////////////////////////////

	static int [] rep(int N) { return rep(0, N); }
	static int [] rep(int S, int T) { int [] res = new int [T-S]; for (int i = S; i < T; ++i) res[i-S] = i; return res; }
	static int [] req(int S, int T) { return rep(S, T+1); }	

	////////////////////////////////////////////////////////////////////////////////////

	/* Dear hacker, don't bother reading below this line, unless you want to help me debug my I/O routines :-) */
	
	final static MyScanner sc = new MyScanner();
	
	static class MyScanner {
		public String next() {
			newLine();
			return line[index++];
		}
		
		public char nextChar() {
			return next().charAt(0);
		}
				
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		
		public String nextLine() {
			line = null;
			return readLine();
		}
		
		public String [] nextStrings() {
			line = null;
			return readLine().split(" ");
		}
		
		public char [] nextChars() {
			return next ().toCharArray ();
		}

		public Integer [] nextInts() {
			String [] L = nextStrings();
			Integer [] res = new Integer [L.length];
			for (int i : rep(L.length))
				res[i] = Integer.parseInt(L[i]);
			return res;
		}	
		
		public Long [] nextLongs() {
			String [] L = nextStrings();
			Long [] res = new Long [L.length];
			for (int i : rep(L.length))
				res[i] = Long.parseLong(L[i]);
			return res;
		}

		public Double [] nextDoubles() {
			String [] L = nextStrings();
			Double [] res = new Double [L.length];
			for (int i : rep(L.length))
				res[i] = Double.parseDouble(L[i]);
			return res;
		}

		public String [] next (int N) {
			String [] res = new String [N];
			for (int i : rep(N))
				res[i] = sc.next();
			return res;
		}
		
		public Integer [] nextInt (int N) {
			Integer [] res = new Integer [N];
			for (int i : rep(N))
				res[i] = sc.nextInt();
			return res;
		}		
		
		public Long [] nextLong (int N) {
			Long [] res = new Long [N];
			for (int i : rep(N))
				res[i] = sc.nextLong();
			return res;
		}		
		
		public Double [] nextDouble (int N) {
			Double [] res = new Double [N];
			for (int i : rep(N))
				res[i] = sc.nextDouble();
			return res;
		}		
		
		public String [][] nextStrings (int N) {
			String [][] res = new String [N][];
			for (int i : rep(N))
				res[i] = sc.nextStrings();
			return res;
		}
		
		public Integer [][] nextInts (int N) {
			Integer [][] res = new Integer [N][];
			for (int i : rep(N))
				res[i] = sc.nextInts();
			return res;
		}
		
		public Long [][] nextLongs (int N) {
			Long [][] res = new Long [N][];
			for (int i : rep(N))
				res[i] = sc.nextLongs();
			return res;
		}
		
		public Double [][] nextDoubles (int N) {
			Double [][] res = new Double [N][];
			for (int i : rep(N))
				res[i] = sc.nextDoubles();
			return res;
		}
		
		//////////////////////////////////////////////
		
		private boolean eol() {
			return index == line.length;
		}

		private String readLine() {
			try {
				return r.readLine();
			} catch (Exception e) {
				throw new Error (e);
			}
		}
		private final java.io.BufferedReader r;

		MyScanner () {
			this(new java.io.BufferedReader(new java.io.InputStreamReader(System.in)));
		}
		
		MyScanner (java.io.BufferedReader r) {
			try {
				this.r = r;
				while (!r.ready())
					Thread.sleep(1);
				start();
			} catch (Exception e) {
				throw new Error(e);
			}
		}
		
		private String [] line;
		private int index;

		private void newLine() {
			if (line == null || eol()) {
				line = readLine().split(" ");
				index = 0;
			}
		}		
	}
	
	static void print (Object o, Object... a) {
		printDelim(" ", o, a);
	}
	
	static void cprint (Object o, Object... a) {
		printDelim("", o, a);
	}
	
	static void printDelim (String delim, Object o, Object... a) {
		pw.println(build(delim, o, a));
	}

	static void exit (Object o, Object... a) {
		print(o, a);
		exit();
	}

	static void exit() {
		pw.close();
		System.out.flush();
		System.err.println("------------------");
		System.err.println("Time: " + ((millis() - t) / 1000.0));
		System.exit(0);
	}
	
	static void NO() {
		throw new Error("NO!");
	}
	
	////////////////////////////////////////////////////////////////////////////////////
	
	static String build (String delim, Object o, Object... a) {
		StringBuilder b = new StringBuilder();
		append(b, o, delim);
		for (Object p : a)
			append(b, p, delim);
		return b.toString().trim();		
	}
	
	static void append(StringBuilder b, Object o, String delim) {
		if (o.getClass().isArray()) {
			int L = java.lang.reflect.Array.getLength(o);
			for (int i : rep(L))
				append(b, java.lang.reflect.Array.get(o, i), delim);
		} else if (o instanceof Iterable<?>) {
			for (Object p : (Iterable<?>)o)
				append(b, p, delim);
		} else
			b.append(delim).append(o);		
	}
	
	////////////////////////////////////////////////////////////////////////////////////
	
	static void statics() {
		abs(0);
		valueOf(0);
		asList(new Object [0]);
		reverseOrder();
	}
	
	public static void main (String[] args) {
		new A();
		exit();
	}

	static void start() {
		t = millis();
	}

	static java.io.PrintWriter pw = new java.io.PrintWriter(System.out, autoflush);
	
	static long t;
	
	static long millis() {
		return System.currentTimeMillis();
	}	
}