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

import static java.lang.Math.*;

public class Solution implements Runnable {

    double sqr(double x) {
        return x * x;
    }

    public void solve() throws Exception {
        int w = sc.nextInt(), h = sc.nextInt(), a = sc.nextInt();
        if (w < h) {
            int temp = w;
            w = h;
            h = temp;
        }
        if (a > 90) {
            a = 180 - a;
        }
        double alpha = PI * a / 180.0;
        double maxalpha = 2 * atan((double) h / w);
        double ans;
        if (a == 0) {
            ans = (double) w * h;
        } else if (alpha <= maxalpha) {
            double r = sqrt(sqr(w) + sqr(h)) / 2.0;
            double h1 = r * sin(maxalpha / 2.0 + alpha) - h / 2.0;
            double h2 = r * cos(maxalpha / 2.0 - alpha) - w / 2.0;
            ans = (double) w * h - (sqr(h1) + sqr(h2)) / (sin(alpha) * cos(alpha));
        } else {
            ans = sqr(h) / tan(alpha) + sqr(h) * tan(alpha / 2.0);
        }
        out.printf(Locale.US, "%.14f\n", ans);
    }

    static Throwable uncaught;

    BufferedReader in;
    FastScanner sc;
    PrintWriter out;

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            solve();
        } catch (Throwable uncaught) {
            Solution.uncaught = uncaught;
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Solution.uncaught != null) {
            throw Solution.uncaught;
        }
    }

}

class FastScanner {

    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }

    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }

}