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

public class C {
	final static double pie = 3.141592653;
	public static void main(String[] argv) throws IOException
	{
		Scanner ins = new Scanner(System.in);//new FileInputStream(new File("./input.txt")));
		PrintStream outs = System.out; //new PrintStream(new File("./input.txt"));

		int w0 = ins.nextInt();
		int h0 = ins.nextInt();
		double w = Math.max(w0, h0);
		double h = Math.min(w0, h0);
		int ang = ins.nextInt();
		if (ang >= 90) ang = 180 - ang;
		double angle = (double)ang / 180 * pie;
		double cri_angle = Math.atan(h/w);
		double hypo = Math.sqrt((double)(w*w+h*h));

		//outs.println(hypo);

		if (angle == 0) outs.println(w*h);
		else if (angle < Math.atan(h/w)*2) {
			double e1 = Math.abs(Math.sin(angle+cri_angle)) * hypo / 2 - h/2;
			double e2 = e1 / Math.abs(Math.sin(angle)) / Math.abs(Math.cos(angle));
			double e3 = w - e2 - e2 * Math.abs(Math.cos(angle));

			//outs.println(180 * (angle+cri_angle)/ pie);
			//outs.println("e1=" + e1);
			//outs.println("e2=" + e2);
			//outs.println("e3=" + e3);

			double tri1 = e3 * e3 / Math.tan(angle) / 2;
			double tri2 = e1 * e2 / 2;

			double area = w * h - 2 * (tri1 + tri2);
			outs.println(area);
		}
		else {
			//outs.println("w=" + w + " h=" + h);
			//outs.println(angle / pie * 180);
			double e1 = w/2.0 - h/2.0/Math.sin(angle);

			//outs.println(e1 + " w="+ w + " h=" + h);

			double area = w*h - e1*h*2.0;
			outs.println(area);
		}

	}
}