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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class con172_C {

	public static void main( final String[] args ) throws Exception {
		if ( DEBUG ) {
			final double dalfa = Math.atan( 2D / 3 );
			System.out.printf( "arctan(2/3)=%f (%f)\n", dalfa, dalfa / Math.PI * 180 );
			final double dalfaPlusBetaSin = Math.sin( dalfa + 30D * Math.PI / 180 );
			System.out.printf( "dalfaPlusBetaSin=%f -> Ny=%f\n", dalfaPlusBetaSin, dalfaPlusBetaSin * Math.sqrt( 13 ) );
		}

		final BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );
		final String line = br.readLine();
		final StringTokenizer tok = new StringTokenizer( line );
		final double w = Integer.parseInt( tok.nextToken() );
		final double h = Integer.parseInt( tok.nextToken() );
		final double alfa = Integer.parseInt( tok.nextToken() );

		System.out.println( solve( Math.max( w, h ), Math.min( w, h ), alfa ) );
	}

	private static final boolean DEBUG = false;

	private static double solve( final double w, final double h, double alfa ) {
		if ( alfa > 90 ) alfa = 180 - alfa;
		if ( alfa == 0 ) {
			return w * h;
		}
		if ( alfa == 90 ) {
			final double min = Math.min( h, w );
			return min * min;
		}
		final double alfaRad = alfa * Math.PI / 180;
		final double tgBeta = h / w;
		final double betaRad = Math.atan( tgBeta );
		if ( DEBUG ) System.out.printf( "betaRad=%f\n", betaRad );
		final double diagPrepPol = Math.sqrt( h * h + w * w ) / 2;
		if ( DEBUG ) System.out.printf( "diagPrepPol=%f\n", diagPrepPol );

		final double Ny = Math.sin( alfaRad + betaRad ) * diagPrepPol;
		final double Nx = Math.cos( alfaRad + betaRad ) * diagPrepPol;
		if ( DEBUG ) System.out.printf( "N=(%f, %f)\n", Nx, Ny );

		final double v = Ny - h / 2;
		final double lp = v / Math.tan( alfaRad );
		final double gama = Math.PI / 2 - alfaRad;

		final double rp = v / Math.tan( gama );

		final double d = w / 2 - Nx - rp;
		if ( DEBUG ) System.out.printf( "d=%f\n", d );
		double res;

		if ( d < 0 ) {
			res = 0;
			final double eps = alfaRad - betaRad;
			if ( DEBUG ) System.out.printf( "eps=%f\n", eps * 180 / Math.PI );
			final double My = Math.sin( eps ) * diagPrepPol;
			if ( DEBUG ) System.out.printf( "My=%f\n", My );
			final double mlp = ( My - h / 2 ) / Math.tan( alfaRad );
			final double mrp = ( My - h / 2 ) / Math.tan( Math.PI / 2 - alfaRad );
			final double part = 1 / 2.0 * ( ( Ny - h / 2 ) * ( lp + rp ) - ( My - h / 2 ) * ( mlp + mrp ) );
			res = w * h - 2 * part;
		} else {
			final double sv = d / Math.tan( alfaRad );
			res = w * h - v * ( lp + rp ) - d * sv;
		}

		return res;
	}

}