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.PrintWriter;
import java.util.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] x = new int[n], y = new int[n];
            for (int i = 0; i < n; i++) {
                x[i] = in.nextInt();
                y[i] = in.nextInt();
            }

            for (int i = 0; i < n; i++) {
                List<Segment> cur = new ArrayList<>();
                cur.add(new Segment(0, 2 * Math.PI));
                for (int j = 0; j < n; j++) {
                    if (i == j) continue;
                    List<Segment> newCur = new ArrayList<>();
                    List<Segment> result = new ArrayList<>();
                    double angle = Math.atan2(y[i] - y[j], x[j] - x[i]);
                    if (angle < 0) {
                        angle += 2 * Math.PI;
                    }

                    if (angle + Math.PI > 2 * Math.PI) {
                        newCur.add(new Segment(angle, 2 * Math.PI));
                        newCur.add(new Segment(0, angle - Math.PI));
                    } else {
                        newCur.add(new Segment(angle, angle + Math.PI));
                    }
                    for (Segment p : cur) {
                        for (Segment q : newCur) {
                            Segment r = p.intersect(q);
                            if (r != null) {
                                result.add(r);
                            }
                        }
                    }

                    cur = result;
                }
                double len = 0;
                for (Segment s : cur) {
                    len += s.r - s.l;
                }
                out.println(len / 2 / Math.PI);
            }
        }

        class Segment {
            double l;
            double r;

            public Segment(double l, double r) {
                this.l = l;
                this.r = r;
            }

            Segment intersect(Segment other) {
                double ll = Math.max(l, other.l), rr = Math.min(r, other.r);
                if (ll >= rr) {
                    return null;
                }
                return new Segment(ll, rr);
            }

        }

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

    }
}