public void solve(int testNumber, FastScanner in, FastPrinter out) {
Circle2DDouble c =
new Circle2DDouble(new Point2DDouble(in.nextInt(), in.nextInt()), in.nextInt());
Point2DDouble p1 = new Point2DDouble(in.nextInt(), in.nextInt());
Point2DDouble p2 = new Point2DDouble(in.nextInt(), in.nextInt());
if (p1.x > p2.x) {
double t = p1.x;
p1.x = p2.x;
p2.x = t;
}
if (p1.y > p2.y) {
double t = p1.y;
p1.y = p2.y;
p2.y = t;
}
List<Point2DDouble> allPoints = new ArrayList<>();
allPoints.add(p1);
allPoints.add(p2);
allPoints.add(new Point2DDouble(p1.x, p2.y));
allPoints.add(new Point2DDouble(p2.x, p1.y));
allPoints.add(new Point2DDouble(c.p.x - c.radius, c.p.y));
allPoints.add(new Point2DDouble(c.p.x + c.radius, c.p.y));
allPoints.add(new Point2DDouble(c.p.x, c.p.y - c.radius));
allPoints.add(new Point2DDouble(c.p.x, c.p.y + c.radius));
for (double x : new double[] {p1.x, p2.x}) {
if (comp.compare(x, c.p.x - c.radius) > 0 && comp.compare(x, c.p.x + c.radius) < 0) {
double dx = c.p.x - x;
double dy = Math.sqrt(c.radius * c.radius - dx * dx);
allPoints.add(new Point2DDouble(x, c.p.y - dy));
allPoints.add(new Point2DDouble(x, c.p.y + dy));
}
}
for (double y : new double[] {p1.y, p2.y}) {
if (comp.compare(y, c.p.y - c.radius) > 0 && comp.compare(y, c.p.y + c.radius) < 0) {
double dy = c.p.y - y;
double dx = Math.sqrt(c.radius * c.radius - dy * dy);
allPoints.add(new Point2DDouble(c.p.x - dx, y));
allPoints.add(new Point2DDouble(c.p.x + dx, y));
}
}
List<Point2DDouble> onRect = new ArrayList<>();
for (Point2DDouble e : allPoints) {
if (inside(p1, p2, e)) {
if (comp.compare(p1.x, e.x) < 0
&& comp.compare(e.x, p2.x) < 0
&& comp.compare(p1.y, e.y) < 0
&& comp.compare(e.y, p2.y) < 0) {
continue;
}
onRect.add(e);
}
}
List<Point2DDouble> onCircle = new ArrayList<>();
for (Point2DDouble e : allPoints) {
if (comp.compare(e.distance(c.p), c.radius) == 0) {
onCircle.add(e);
}
}
final Point2DDouble centerRect = p1.add(p2).multiply(0.5);
Collections.sort(
onRect,
new Comparator<Point2DDouble>() {
int get(Point2DDouble e) {
int x = comp.compare(e.x, 0);
int y = comp.compare(e.y, 0);
if (x > 0) {
return y > 0 ? 2 : y < 0 ? 8 : 1;
} else if (x < 0) {
return y > 0 ? 4 : y < 0 ? 6 : 5;
} else {
return y > 0 ? 3 : y < 0 ? 7 : 0;
}
}
@Override
public int compare(Point2DDouble o1, Point2DDouble o2) {
o1 = o1.subtract(centerRect);
o2 = o2.subtract(centerRect);
int c = get(o1) - get(o2);
if (c != 0) return c;
return comp.compare(o2.vmul(o1), 0);
}
});
final Point2DDouble circleCenter = c.p;
Collections.sort(
onCircle,
new Comparator<Point2DDouble>() {
int get(Point2DDouble e) {
int x = comp.compare(e.x, 0);
int y = comp.compare(e.y, 0);
if (x > 0) {
return y > 0 ? 2 : y < 0 ? 8 : 1;
} else if (x < 0) {
return y > 0 ? 4 : y < 0 ? 6 : 5;
} else {
return y > 0 ? 3 : y < 0 ? 7 : 0;
}
}
@Override
public int compare(Point2DDouble o1, Point2DDouble o2) {
o1 = o1.subtract(circleCenter);
o2 = o2.subtract(circleCenter);
int c = get(o1) - get(o2);
if (c != 0) return c;
return comp.compare(o2.vmul(o1), 0);
}
});
List<Segment> allSegments = new ArrayList<>();
for (int i = 0; i < onRect.size(); i++) {
Point2DDouble r1 = onRect.get(i);
Point2DDouble r2 = onRect.get((i + 1) % onRect.size());
if (pointsEqual(r1, r2)) continue;
Point2DDouble r0 = r1.add(r2).multiply(0.5);
if (comp.compare(r0.distance(c.p), c.radius) < 0) {
allSegments.add(new Segment(r1, r2, 0));
}
}
for (int i = 0; i < onCircle.size(); i++) {
Point2DDouble r1 = onCircle.get(i);
Point2DDouble r2 = onCircle.get((i + 1) % onCircle.size());
if (pointsEqual(r1, r2)) continue;
r1 = r1.subtract(c.p);
r2 = r2.subtract(c.p);
Point2DDouble r0 = r1.add(r2);
r0 = r0.multiply(c.radius / r0.length());
r0 = r0.add(c.p);
if (inside(p1, p2, r0)) {
allSegments.add(new Segment(r1.add(c.p), r2.add(c.p), c.radius));
}
}
if (allSegments.isEmpty()) {
out.println(0);
return;
}
boolean[] was = new boolean[allSegments.size()];
List<Segment> sortedSegments = new ArrayList<>();
sortedSegments.add(allSegments.get(0));
was[0] = true;
Point2DDouble last = sortedSegments.get(sortedSegments.size() - 1).q;
// System.out.println(allSegments);
while (!pointsEqual(sortedSegments.get(0).p, last)) {
int id = -1;
for (int i = 0; i < allSegments.size(); i++) {
if (was[i]) continue;
Segment e = allSegments.get(i);
if (pointsEqual(e.p, last)) {
id = i;
break;
}
}
if (id < 0) throw new AssertionError();
was[id] = true;
sortedSegments.add(allSegments.get(id));
last = allSegments.get(id).q;
}
double area = 0;
for (Segment e : sortedSegments) {
area += e.p.vmul(e.q);
}
area = Math.abs(area) * .5;
for (Segment e : sortedSegments) {
if (comp.compare(e.r, 0) > 0) {
double dist = e.p.distance(e.q);
double sin = dist * .5 / c.radius;
if (sin > 1) sin = 1;
else if (sin < -1) sin = -1;
double ang = Math.asin(sin) * 2;
area += c.radius * c.radius * .5 * (ang - Math.sin(ang));
}
}
out.println(area);
}
