import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public final class TotalCirclesArea {

	public static void main(String[] args) {
		final double precision = 0.000_001;
		System.out.println(String.format("%s%.8f", "Approximate area = ", areaScan(precision)));
	}
	
	private static double areaScan(double precision) {
		List<Double> valuesY = new ArrayList<Double>();
		for ( Circle circle : circles ) {
			valuesY.add(circle.centreY + circle.radius);
		}
		for ( Circle circle : circles ) {
			valuesY.add(circle.centreY - circle.radius);
		}
		
		final double min = valuesY.stream().min(Double::compare).get();
		final double max = valuesY.stream().max(Double::compare).get();
		final long minY = (long) Math.floor(min / precision);
		final long maxY = (long) Math.ceil(max / precision);

	    double totalArea = 0.0;
	    for ( long i = minY; i <= maxY; i++ ) {
	    	final double y = i * precision;
	    	double right = Double.NEGATIVE_INFINITY;

	    	List<PairX> pairsX = new ArrayList<PairX>();
	    	for ( Circle circle : circles ) {
	    		if ( Math.abs(y - circle.centreY) < circle.radius ) {
	    			pairsX.add(horizontalSection(circle, y));
	    		}
	    	}
	    	Collections.sort(pairsX, (one, two) -> Double.compare(one.x1, two.x1) );

	    	for ( PairX pairX : pairsX ) {
				if ( pairX.x2 > right ) {
					totalArea += pairX.x2 - Math.max(pairX.x1, right);
					right = pairX.x2;
				}
			}
	    }
	    return totalArea * precision;
	}
	
	private static PairX horizontalSection(Circle circle, double y) {
		final double value = circle.radius * circle.radius - ( y - circle.centreY ) * ( y - circle.centreY );
		final double deltaX = Math.sqrt(value);
		return new PairX(circle.centreX - deltaX, circle.centreX + deltaX);
	}
	
	private static record PairX(double x1, double x2) {}
	private static record Circle(double centreX, double centreY, double radius) {}
	
	private static final List<Circle> circles = List.of(
		new Circle( 1.6417233788,  1.6121789534, 0.0848270516),
		new Circle(-1.4944608174,  1.2077959613, 1.1039549836),
		new Circle( 0.6110294452, -0.6907087527, 0.9089162485),
		new Circle( 0.3844862411,  0.2923344616, 0.2375743054),
		new Circle(-0.2495892950, -0.3832854473, 1.0845181219),
		new Circle( 1.7813504266,  1.6178237031, 0.8162655711),
		new Circle(-0.1985249206, -0.8343333301, 0.0538864941),
		new Circle(-1.7011985145, -0.1263820964, 0.4776976918),
		new Circle(-0.4319462812,  1.4104420482, 0.7886291537),
		new Circle( 0.2178372997, -0.9499557344, 0.0357871187),
		new Circle(-0.6294854565, -1.3078893852, 0.7653357688),
		new Circle( 1.7952608455,  0.6281269104, 0.2727652452),
		new Circle( 1.4168575317,  1.0683357171, 1.1016025378),
		new Circle( 1.4637371396,  0.9463877418, 1.1846214562),
		new Circle(-0.5263668798,  1.7315156631, 1.4428514068),
		new Circle(-1.2197352481,  0.9144146579, 1.0727263474),
		new Circle(-0.1389358881,  0.1092805780, 0.7350208828),
		new Circle( 1.5293954595,  0.0030278255, 1.2472867347),
		new Circle(-0.5258728625,  1.3782633069, 1.3495508831),
		new Circle(-0.1403562064,  0.2437382535, 1.3804956588),
		new Circle( 0.8055826339, -0.0482092025, 0.3327165165),
		new Circle(-0.6311979224,  0.7184578971, 0.2491045282),
		new Circle( 1.4685857879, -0.8347049536, 1.3670667538),
		new Circle(-0.6855727502,  1.6465021616, 1.0593087096),
		new Circle( 0.0152957411,  0.0638919221, 0.9771215985)
	);

}