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:
// package agc.agc021;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n = in.nextInt();
        long[][] pt = new long[n][2];
        for (int i = 0; i < n ; i++) {
            for (int j = 0; j < 2 ; j++) {
                pt[i][j] = in.nextLong();
            }
        }
        double[] ret = solve(pt);
        for (double d : ret) {
            out.println(String.format("%.12f", d));
        }
        out.flush();
    }

    private static double[] solve(long[][] pt) {
        int n = pt.length;
        if (n == 2) {
            return new double[]{0.5, 0.5};
        }

        Point[] points = new Point[n];
        for (int i = 0; i < n ; i++) {
            points[i] = new Point(i, pt[i][0], pt[i][1]);
        }
        List<Point> hull = convexHull(points);

        double[] possibility = new double[n];
        int hn = hull.size();
        for (int i = 0; i < hn ; i++) {
            Point c = hull.get(i);
            Point a = hull.get((i-1+hn)%hn);
            Point b = hull.get((i+1)%hn);
            double ax = a.x - c.x;
            double ay = a.y - c.y;
            double bx = b.x - c.x;
            double by = b.y - c.y;
            double cross = ax * bx + ay * by;
            double norm = Math.hypot(ax, ay) * Math.hypot(bx, by);
            double cos = Math.max(-1, Math.min(1, cross / norm));

            double rad = Math.acos(cos);
            double rate = Math.PI - rad;
            possibility[c.id] = rate / (Math.PI * 2);
        }
        return possibility;
    }

    static class Point implements Comparable<Point> {
        int id;
        long x;
        long y;

        Point(int i, long _x, long _y) {
            id = i;
            x = _x;
            y = _y;
        }

        Point(Point a, Point b) {
            x = b.x - a.x;
            y = b.y - a.y;
        }

        public int compareTo(Point o) {
            if (x != o.x) {
                return Long.signum(x - o.x);
            }
            return Long.signum(y - o.y);
        }

        public long det(Point other) {
            return x * other.y - y * other.x;
        }

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

    public static List<Point> convexHull(Point[] points) {
        int n = points.length;
        Arrays.sort(points);
        Point[] candidate = new Point[n * 2];
        int k = 0;

        // downer
        for (int i = 0; i < n; i++) {
            while (k > 1) {
                Point a = new Point(candidate[k - 2], candidate[k - 1]);
                Point b = new Point(candidate[k - 1], points[i]);
                if (a.det(b) <= 0) {
                    k--;
                } else {
                    break;
                }
            }
            candidate[k++] = points[i];
        }

        // upper
        int t = k;
        for (int i = n - 2; i >= 0; i--) {
            while (k > t) {
                Point a = new Point(candidate[k - 2], candidate[k - 1]);
                Point b = new Point(candidate[k - 1], points[i]);
                if (a.det(b) <= 0) {
                    k--;
                } else {
                    break;
                }
            }
            candidate[k++] = points[i];
        }
        List<Point> ret = new ArrayList<>();
        for (int i = 0; i < k - 1; i++) {
            ret.add(candidate[i]);
        }
        return ret;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

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

        private int next() {
            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 char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

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

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

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