In Berland a bus travels along the main street of the capital. The street begins from the main square and looks like a very long segment. There are n bus stops located along the street, the i-th of them is located at the distance ai from the central square, all distances are distinct, the stops are numbered in the order of increasing distance from the square, that is, ai < ai + 1 for all i from 1 to n - 1. The bus starts its journey from the first stop, it passes stops 2, 3 and so on. It reaches the stop number n, turns around and goes in the opposite direction to stop 1, passing all the intermediate stops in the reverse order. After that, it again starts to move towards stop n. During the day, the bus runs non-stop on this route.

The bus is equipped with the Berland local positioning system. When the bus passes a stop, the system notes down its number.

One of the key features of the system is that it can respond to the queries about the distance covered by the bus for the parts of its path between some pair of stops. A special module of the system takes the input with the information about a set of stops on a segment of the path, a stop number occurs in the set as many times as the bus drove past it. This module returns the length of the traveled segment of the path (or -1 if it is impossible to determine the length uniquely). The operation of the module is complicated by the fact that stop numbers occur in the request not in the order they were visited but in the non-decreasing order.

For example, if the number of stops is 6, and the part of the bus path starts at the bus stop number 5, ends at the stop number 3 and passes the stops as follows: <image>, then the request about this segment of the path will have form: 3, 4, 5, 5, 6. If the bus on the segment of the path from stop 5 to stop 3 has time to drive past the 1-th stop (i.e., if we consider a segment that ends with the second visit to stop 3 on the way from 5), then the request will have form: 1, 2, 2, 3, 3, 4, 5, 5, 6.

You will have to repeat the Berland programmers achievement and implement this function.

Input

The first line contains integer n (2 ≤ n ≤ 2·105) — the number of stops.

The second line contains n integers (1 ≤ ai ≤ 109) — the distance from the i-th stop to the central square. The numbers in the second line go in the increasing order.

The third line contains integer m (1 ≤ m ≤ 4·105) — the number of stops the bus visited on some segment of the path.

The fourth line contains m integers (1 ≤ bi ≤ n) — the sorted list of numbers of the stops visited by the bus on the segment of the path. The number of a stop occurs as many times as it was visited by a bus.

It is guaranteed that the query corresponds to some segment of the path.

Output

In the single line please print the distance covered by a bus. If it is impossible to determine it unambiguously, print  - 1.

Examples

Input

6
2 3 5 7 11 13
5
3 4 5 5 6


Output

10


Input

6
2 3 5 7 11 13
9
1 2 2 3 3 4 5 5 6


Output

16


Input

3
10 200 300
4
1 2 2 3


Output

-1


Input

3
1 2 3
4
1 2 2 3


Output

3

Note

The first test from the statement demonstrates the first example shown in the statement of the problem.

The second test from the statement demonstrates the second example shown in the statement of the problem.

In the third sample there are two possible paths that have distinct lengths, consequently, the sought length of the segment isn't defined uniquely.

In the fourth sample, even though two distinct paths correspond to the query, they have the same lengths, so the sought length of the segment is defined uniquely.
import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {

	int[] count, aux;
	Set<Integer> diff;
	
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int n=in.readInt(), last=0;
		int[] A=new int[n];
		count=new int[n];
		aux=new int[n];
		aux[0]=1;
		for (int i=0; i<n; i++) A[i]=in.readInt();
		int m=in.readInt();
		for (int i=0; i<m; i++) count[in.readInt()-1]++;
		long total=0;
		diff=new TreeSet<>();
		Set<Long> ret=new TreeSet<>();
		boolean asc=true;
		for (int i=1; i<m; i++) {
			if (asc) {
				total+=A[last+1]-A[last++];
				if (last==n-1) asc=false;
			} else {
				total+=A[last]-A[--last];
				if (last==0) asc=true;
			}
			aux[last]++;
		}
		for (int i=0; i<n; i++) f(i);
		if (diff.isEmpty()) ret.add(total);
		for (int i=1; i<n; i++) {
			aux[i-1]--;
			total+=A[i-1]-A[i];
			if (asc) {
				total+=A[last+1]-A[last++];
				if (last==n-1) asc=false;
			} else {
				total+=A[last]-A[--last];
				if (last==0) asc=true;
			}
			aux[last]++;
			f(i-1);
			f(last);
			if (diff.isEmpty()) ret.add(total);
//			out.printLine(count);
//			out.printLine(aux);
//			out.printLine(diff);
//			out.printLine(total);
//			out.printLine(ret);
//			out.printLine();
		}
		for (int i=n-2; i>0; i--) {
			aux[i+1]--;
			total+=A[i]-A[i+1];
			if (asc) {
				total+=A[last+1]-A[last++];
				if (last==n-1) asc=false;
			} else {
				total+=A[last]-A[--last];
				if (last==0) asc=true;
			}
			aux[last]++;
			f(i+1);
			f(last);
			if (diff.isEmpty()) ret.add(total);
//			out.printLine(count);
//			out.printLine(aux);
//			out.printLine(diff);
//			out.printLine(total);
//			out.printLine(ret);
//			out.printLine();
		}
		if (ret.size()==1) out.printLine(ret.toArray());
		else out.printLine(-1);
	}
	
	void f(int i) {
		if (count[i]==aux[i]) diff.remove(i);
		else diff.add(i);
	}
}

class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}

	public String next() {
		return readString();
	}

	public SpaceCharFilter getFilter() {
		return filter;
	}

	public void setFilter(SpaceCharFilter filter) {
		this.filter = filter;
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(char[] array) {
		writer.print(array);
	}

	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void print(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(array[i]);
		}
	}

	public void print(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(array[i]);
		}
	}

	public void print(Collection<Integer> collection) {
		boolean first = true;
		for (int i : collection) {
			if (first)
				first = false;
			else
				writer.print(' ');
			writer.print(i);
		}
	}

	public void printLine(int[] array) {
		print(array);
		writer.println();
	}

	public void printLine(long[] array) {
		print(array);
		writer.println();
	}

	public void printLine(Collection<Integer> collection) {
		print(collection);
		writer.println();
	}

	public void printLine() {
		writer.println();
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void print(char i) {
		writer.print(i);
	}

	public void printLine(char i) {
		writer.println(i);
	}

	public void printLine(char[] array) {
		writer.println(array);
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}

	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}

	public void print(long i) {
		writer.print(i);
	}

	public void printLine(long i) {
		writer.println(i);
	}

	public void print(int i) {
		writer.print(i);
	}

	public void printLine(int i) {
		writer.println(i);
	}
}

class Polygon {
    public final Point[] vertices;
    private Segment[] sides;

    public Polygon(Point...vertices) {
            this.vertices = vertices.clone();
    }

    public double square() {
            double sum = 0;
            for (int i = 1; i < vertices.length; i++)
                    sum += (vertices[i].x - vertices[i - 1].x) * (vertices[i].y + vertices[i - 1].y);
            sum += (vertices[0].x - vertices[vertices.length - 1].x) * (vertices[0].y + vertices[vertices.length - 1].y);
            return Math.abs(sum) / 2;
    }

    public Point center() {
            double sx = 0;
            double sy = 0;
            for (Point point : vertices) {
                    sx += point.x;
                    sy += point.y;
            }
            return new Point(sx / vertices.length, sy / vertices.length);
    }

public static boolean over(Point a, Point b, Point c) {
    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < -GeometryUtils.epsilon;
}

private static boolean under(Point a, Point b, Point c) {
    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > GeometryUtils.epsilon;
}

public static Polygon convexHull(Point[] points) {
    if (points.length == 1)
        return new Polygon(points);
    Arrays.sort(points, new Comparator<Point>() {
        public int compare(Point o1, Point o2) {
            int value = Double.compare(o1.x, o2.x);
            if (value != 0)
                return value;
            return Double.compare(o1.y, o2.y);
        }
    });
    Point left = points[0];
    Point right = points[points.length - 1];
    List<Point> up = new ArrayList<Point>();
    List<Point> down = new ArrayList<Point>();
    for (Point point : points) {
        if (point == left || point == right || !under(left, point, right)) {
            while (up.size() >= 2 && under(up.get(up.size() - 2), up.get(up.size() - 1), point))
                up.remove(up.size() - 1);
            up.add(point);
        }
        if (point == left || point == right || !over(left, point, right)) {
            while (down.size() >= 2 && over(down.get(down.size() - 2), down.get(down.size() - 1), point))
                down.remove(down.size() - 1);
            down.add(point);
        }
    }
    Point[] result = new Point[up.size() + down.size() - 2];
    int index = 0;
    for (Point point : up)
        result[index++] = point;
    for (int i = down.size() - 2; i > 0; i--)
        result[index++] = down.get(i);
    return new Polygon(result);
}

    public boolean contains(Point point) {
            return contains(point, false);
    }

public boolean contains(Point point, boolean strict) {
            for (Segment segment : sides()) {
                    if (segment.contains(point, true))
                            return !strict;
            }
    double totalAngle = GeometryUtils.canonicalAngle(Math.atan2(vertices[0].y - point.y, vertices[0].x - point.x) -
                    Math.atan2(vertices[vertices.length - 1].y - point.y, vertices[vertices.length - 1].x - point.x));
    for (int i = 1; i < vertices.length; i++) {
        totalAngle += GeometryUtils.canonicalAngle(Math.atan2(vertices[i].y - point.y, vertices[i].x - point.x) -
                            Math.atan2(vertices[i - 1].y - point.y, vertices[i - 1].x - point.x));
    }
    return Math.abs(totalAngle) > Math.PI;
}

    public Segment[] sides() {
            if (sides == null) {
                    sides = new Segment[vertices.length];
                    for (int i = 0; i < vertices.length - 1; i++)
                            sides[i] = new Segment(vertices[i], vertices[i + 1]);
                    sides[sides.length - 1] = new Segment(vertices[vertices.length - 1], vertices[0]);
            }
            return sides;
    }

    public static double triangleSquare(Point a, Point b, Point c) {
            return Math.abs((a.x - b.x) * (a.y + b.y) + (b.x - c.x) * (b.y + c.y) + (c.x - a.x) * (c.y + a.y)) / 2;
    }

    public double perimeter() {
            double result = vertices[0].distance(vertices[vertices.length - 1]);
            for (int i = 1; i < vertices.length; i++)
                    result += vertices[i].distance(vertices[i - 1]);
            return result;
    }
}

class Point {
    public static final Point ORIGIN = new Point(0, 0);
    public final double x;
    public final double y;

    @Override
    public String toString() {
            return "(" + x + ", " + y + ")";
    }

    public Point(double x, double y) {
            this.x = x;
            this.y = y;
    }

    public Line line(Point other) {
            if (equals(other))
                    return null;
            double a = other.y - y;
            double b = x - other.x;
            double c = -a * x - b * y;
            return new Line(a, b, c);
    }

    @Override
    public boolean equals(Object o) {
            if (this == o)
                    return true;
            if (o == null || getClass() != o.getClass())
                    return false;

            Point point = (Point) o;

            return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
    }

    @Override
    public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
    }

    public double distance(Point other) {
            return GeometryUtils.fastHypot(x - other.x, y - other.y);
    }

    public double distance(Line line) {
            return Math.abs(line.a * x + line.b * y + line.c);
    }

    public double value() {
            return GeometryUtils.fastHypot(x, y);
    }

    public double angle() {
            return Math.atan2(y, x);
    }

    public static Point readPoint(InputReader in) {
            double x = in.readDouble();
            double y = in.readDouble();
            return new Point(x, y);
    }

    public Point rotate(double angle) {
            double nx = x * Math.cos(angle) - y * Math.sin(angle);
            double ny = y * Math.cos(angle) + x * Math.sin(angle);
            return new Point(nx, ny);
    }
}

class Segment {
    public final Point a;
    public final Point b;
private double distance = Double.NaN;
private Line line = null;

    public Segment(Point a, Point b) {
            this.a = a;
            this.b = b;
    }

    public double length() {
    if (Double.isNaN(distance))
        distance = a.distance(b);
    return distance;
    }

    public double distance(Point point) {
            double length = length();
            double left = point.distance(a);
            if (length < GeometryUtils.epsilon)
                    return left;
            double right = point.distance(b);
            if (left * left > right * right + length * length)
                    return right;
            if (right * right > left * left + length * length)
                    return left;
            return point.distance(line());
    }

    public Point intersect(Segment other, boolean includeEnds) {
            Line line = line();
            Line otherLine = other.a.line(other.b);
            if (line.parallel(otherLine))
                    return null;
            Point intersection = line.intersect(otherLine);
            if (contains(intersection, includeEnds) && other.contains(intersection, includeEnds))
                    return intersection;
            else
                    return null;
    }

    public boolean contains(Point point, boolean includeEnds) {
            if (a.equals(point) || b.equals(point))
                    return includeEnds;
            if (a.equals(b))
                    return false;
            Line line = line();
            if (!line.contains(point))
                    return false;
            Line perpendicular = line.perpendicular(a);
            double aValue = perpendicular.value(a);
            double bValue = perpendicular.value(b);
            double pointValue = perpendicular.value(point);
            return aValue < pointValue && pointValue < bValue || bValue < pointValue && pointValue < aValue;
    }

    public Line line() {
    if (line == null)
        line = a.line(b);
            return line;
    }

    public Point middle() {
            return new Point((a.x + b.x) / 2, (a.y + b.y) / 2);
    }

    public Point[] intersect(Circle circle) {
            Point[] result = line().intersect(circle);
            if (result.length == 0)
                    return result;
            if (result.length == 1) {
                    if (contains(result[0], true))
                            return result;
                    return new Point[0];
            }
            if (contains(result[0], true)) {
                    if (contains(result[1], true))
                            return result;
                    return new Point[]{result[0]};
            }
            if (contains(result[1], true))
                    return new Point[]{result[1]};
            return new Point[0];
    }

    public Point intersect(Line line) {
            Line selfLine = line();
            Point intersect = selfLine.intersect(line);
            if (intersect == null)
                    return null;
            if (contains(intersect, true))
                    return intersect;
            return null;
    }

    public double distance(Segment other) {
            Line line = line();
            Line otherLine = other.line();
            Point p = line == null || otherLine == null ? null : line.intersect(otherLine);
            if (p != null && contains(p, true) && other.contains(p, true))
                    return 0;
            return Math.min(Math.min(other.distance(a), other.distance(b)), Math.min(distance(other.a), distance(other.b)));
    }
}

class GeometryUtils {
    public static double epsilon = 1e-8;

    public static double fastHypot(double...x) {
            if (x.length == 0)
                    return 0;
            else if (x.length == 1)
                    return Math.abs(x[0]);
            else {
                    double sumSquares = 0;
                    for (double value : x)
                            sumSquares += value * value;
                    return Math.sqrt(sumSquares);
            }
    }

public static double fastHypot(double x, double y) {
    return Math.sqrt(x * x + y * y);
}

    public static double fastHypot(double[] x, double[] y) {
            if (x.length == 0)
                    return 0;
            else if (x.length == 1)
                    return Math.abs(x[0]- y[0]);
            else {
                    double sumSquares = 0;
                    for (int i = 0; i < x.length; i++) {
                            double diff = x[i] - y[i];
                            sumSquares += diff * diff;
                    }
                    return Math.sqrt(sumSquares);
            }
    }

    public static double fastHypot(int[] x, int[] y) {
            if (x.length == 0)
                    return 0;
            else if (x.length == 1)
                    return Math.abs(x[0]- y[0]);
            else {
                    double sumSquares = 0;
                    for (int i = 0; i < x.length; i++) {
                            double diff = x[i] - y[i];
                            sumSquares += diff * diff;
                    }
                    return Math.sqrt(sumSquares);
            }
    }

    public static double missileTrajectoryLength(double v, double angle, double g) {
            return (v * v * Math.sin(2 * angle)) / g;
    }

    public static double sphereVolume(double radius) {
            return 4 * Math.PI * radius * radius * radius / 3;
    }

    public static double triangleSquare(double first, double second, double third) {
            double p = (first + second + third) / 2;
            return Math.sqrt(p * (p - first) * (p - second) * (p - third));
    }

    public static double canonicalAngle(double angle) {
            while (angle > Math.PI)
                    angle -= 2 * Math.PI;
            while (angle < -Math.PI)
                    angle += 2 * Math.PI;
            return angle;
    }

    public static double positiveAngle(double angle) {
            while (angle > 2 * Math.PI - GeometryUtils.epsilon)
                    angle -= 2 * Math.PI;
            while (angle < -GeometryUtils.epsilon)
                    angle += 2 * Math.PI;
            return angle;
    }
}

class Line {
    public final double a;
    public final double b;
    public final double c;

    public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
    }

    public Line(double a, double b, double c) {
            double h = GeometryUtils.fastHypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
    }

    public Point intersect(Line other) {
            if (parallel(other))
                    return null;
            double determinant = b * other.a - a * other.b;
            double x = (c * other.b - b * other.c) / determinant;
            double y = (a * other.c - c * other.a) / determinant;
            return new Point(x, y);
    }

    public boolean parallel(Line other) {
            return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
    }

    public boolean contains(Point point) {
            return Math.abs(value(point)) < GeometryUtils.epsilon;
    }

    public Line perpendicular(Point point) {
            return new Line(-b, a, b * point.x - a * point.y);
    }

    public double value(Point point) {
            return a * point.x + b * point.y + c;
    }

    public Point[] intersect(Circle circle) {
            double distance = distance(circle.center);
            if (distance > circle.radius + GeometryUtils.epsilon)
                    return new Point[0];
            Point intersection = intersect(perpendicular(circle.center));
            if (Math.abs(distance - circle.radius) < GeometryUtils.epsilon)
                    return new Point[]{intersection};
            double shift = Math.sqrt(circle.radius * circle.radius - distance * distance);
            return new Point[]{new Point(intersection.x + shift * b, intersection.y - shift * a),
                    new Point(intersection.x - shift * b, intersection.y + shift * a)};
    }

    public double distance(Point center) {
            return Math.abs(value(center));
    }

    @Override
    public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Line line = (Line) o;

            if (!parallel(line)) return false;
            if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon || Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon) return false;

            return true;
    }
}

class Circle {
    public final Point center;
    public final double radius;

    public Circle(Point center, double radius) {
            this.center = center;
            this.radius = radius;
    }

    public boolean contains(Point point) {
            return center.distance(point) < radius + GeometryUtils.epsilon;
    }

    public boolean strictContains(Point point) {
            return center.distance(point) < radius - GeometryUtils.epsilon;
    }

public Point[] findTouchingPoints(Point point) {
    double distance = center.distance(point);
    if (distance < radius - GeometryUtils.epsilon)
        return new Point[0];
    if (distance < radius + GeometryUtils.epsilon)
        return new Point[]{point};
    Circle power = new Circle(point, Math.sqrt((distance - radius) * (distance + radius)));
    return intersect(power);
}

public Point[] intersect(Circle other) {
    double distance = center.distance(other.center);
    if (distance > radius + other.radius + GeometryUtils.epsilon || Math.abs(radius - other.radius) > distance + GeometryUtils.epsilon)
        return new Point[0];
    double p = (radius + other.radius + distance) / 2;
    double height = 2 * Math.sqrt(p * (p - radius) * (p - other.radius) * (p - distance)) / distance;
    double l1 = Math.sqrt(radius * radius - height * height);
    double l2 = Math.sqrt(other.radius * other.radius - height * height);
    if (radius * radius + distance * distance < other.radius * other.radius)
        l1 = -l1;
    if (radius * radius > distance * distance + other.radius * other.radius)
        l2 = -l2;
    Point middle = new Point((center.x * l2 + other.center.x * l1) / (l1 + l2),
        (center.y * l2 + other.center.y * l1) / (l1 + l2));
    Line line = center.line(other.center).perpendicular(middle);
    return line.intersect(this);
}
}