Problem: There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).

Let R=10^{10^{10^{10}}}. Ringo performs the following operation:

* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.



For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.

Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:

* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Constraints

* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.

The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.

Examples

Input

2
0 0
1 1


Output

0.5
0.5


Input

5
0 0
2 8
4 5
2 6
3 10


Output

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            Point[] p = new Point[n];
            for (int i = 0; i < n; i++) {
                p[i] = Point.readPoint(in);
            }
            double[] answer = new double[n];
            Polygon pol = Polygon.convexHull(p.clone());
            for (int i = 0; i < pol.vertices.length; i++) {
                int prev = i - 1;
                if (prev < 0) {
                    prev += pol.vertices.length;
                }
                int next = i + 1;
                if (next >= pol.vertices.length) {
                    next -= pol.vertices.length;
                }
                double ang1 = new Vector(pol.vertices[prev], pol.vertices[i]).angle();
                double ang2 = new Vector(pol.vertices[i], pol.vertices[next]).angle();
                double ang = ang1 - ang2;
                if (ang < 0) {
                    ang += 2 * Math.PI;
                }
                for (int j = 0; j < n; j++) {
                    if (p[j].equals(pol.vertices[i])) {
                        answer[j] = ang / (2 * Math.PI);
                    }
                }
            }
            for (double d : answer) {
                out.printLine(d);
            }
        }

    }

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

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

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

    }

    static class Polygon {
        public final Point[] vertices;

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

        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);
        }

    }

    static class Vector {
        public final double x;
        public final double y;
        public final Point point;

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

        public Vector(Point point) {
            this.x = point.x;
            this.y = point.y;
            this.point = point;
        }

        public Vector(Point from, Point to) {
            this(to.x - from.x, to.y - from.y);
        }

        public double angle() {
            return point.angle();
        }

    }

    static class Point {
        public final double x;
        public final double y;


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

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


        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;
        }


        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 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);
        }

    }

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

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.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 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 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;
        }

        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 interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}