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.util.Arrays.deepToString;

import java.io.*;
import java.math.*;
import java.util.*;

import static java.lang.Math.PI;
import static java.lang.Math.atan;
import static java.lang.Math.cos;
import static java.lang.Math.sin;
import static java.lang.Math.tan;

public class A {

	final static double eps = 1e-10;

	static void solve() {
		double w = nextInt(), h = nextInt();
		int alpha = nextInt();
		if (alpha > 90) {
			alpha = 180 - alpha;
		}
		if (w < h) {
			double tmp = w;
			w = h;
			h = tmp;
		}
		double phi = atan(w / h); // phi >= PI / 2
		double alp = alpha * PI / 180;
		double d = Math.hypot(w / 2, h / 2);
		double ans = w * h;
		if (alpha == 0) {
			writer.println(ans);
			return;
		}
		if (alp <= PI - 2 * phi) {
			double[] pt = rotate(new double[] { w / 2, -h / 2 }, alp);
			double[] v = rotate(new double[] { 0, h }, alp);
			double len = h / 2 - y_intersect(w / 2, pt, v);
			double area = len * len * tan(alp) / 2;
			pt = rotate(new double[] { w / 2, h / 2 }, alp);
			v = rotate(new double[] { w, 0 }, alp);
			len = w / 2 + x_intersect(h / 2, pt, v);
			area += len * len * tan(alp) / 2;
			ans -= 2 * area;
		} else {
			double[] pt = rotate(new double[] { w / 2, -h / 2 }, alp);
			double[] v = rotate(new double[] { w, 0 }, alp);
			double len1 = w / 2 - x_intersect(h / 2, pt, v);
			double len2 = w / 2 - x_intersect(-h / 2, pt, v);
			ans -= h * (len1 + len2);
		}
		writer.println(ans);
	}

	static double[] rotate(double[] v, double phi) {
		return new double[] { v[0] * cos(phi) - v[1] * sin(phi), v[0] * sin(phi) + v[1] * cos(phi) };
	}

	static double x_intersect(double y, double[] pt, double[] v) {
		double t = (y - pt[1]) / v[1];
		return pt[0] + v[0] * t;
	}

	static double y_intersect(double x, double[] pt, double[] v) {
		double t = (x - pt[0]) / v[0];
		return pt[1] + v[1] * t;
	}

	public static void main(String[] args) throws Exception {
		reader = new BufferedReader(new InputStreamReader(System.in));
		writer = new PrintWriter(System.out);
		Locale.setDefault(Locale.US);

		setTime();
		solve();
		printTime();
		printMemory();

		writer.close();
	}

	static BufferedReader reader;
	static PrintWriter writer;
	static StringTokenizer tok = new StringTokenizer("");
	static long systemTime;

	static void debug(Object... o) {
		System.err.println(deepToString(o));
	}

	static void setTime() {
		systemTime = System.currentTimeMillis();
	}

	static void printTime() {
		System.err.println("Time consumed: " + (System.currentTimeMillis() - systemTime));
	}

	static void printMemory() {
		System.err.println("Memory consumed: "
				+ (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) / 1000 + "kb");
	}

	static String next() {
		while (!tok.hasMoreTokens()) {
			String w = null;
			try {
				w = reader.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			if (w == null)
				return null;
			tok = new StringTokenizer(w);
		}
		return tok.nextToken();
	}

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

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

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static BigInteger nextBigInteger() {
		return new BigInteger(next());
	}
}