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.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.stream.Stream;
import java.util.StringTokenizer;
import java.util.Optional;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.LinkedList;
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;
        MyScan in = new MyScan(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, MyScan in, PrintWriter out) {
            int n = in.nextInt();
            int[][] pp = new int[n][3];
            for (int s = 0; s < n; s++) {
                pp[s][0] = in.nextInt();
                pp[s][1] = in.nextInt();
                pp[s][2] = s;
            }
            ConvexHull convexHull = new ConvexHull();
            pp = convexHull.calculate(pp);
            double[] res = new double[n];
            for (int i = 0; i < pp.length; i++) {
                int li = (i - 1 + pp.length) % pp.length;
                int ri = (i + 1 + pp.length) % pp.length;

                int[] v11 = ConvexHull.v1(pp[i], pp[li]);
                int[] v12 = ConvexHull.v1(pp[i], pp[ri]);

                res[pp[i][2]] = (Math.PI - ConvexHull.angle(v11, v12)) / 2 / Math.PI;

            }


            for (int i = 0; i < n; i++) {
                out.println(res[i]);
            }
        }

    }

    static class ConvexHull {
        public int[][] calculate(int[][] points) {
            int n = points.length;
            int[] right = Arrays.stream(points).min(Comparator.<int[]>comparingInt(t -> -t[0]).thenComparing(t -> t[1])).get();
            long[] dist = new long[n];
            for (int i = 0; i < n; i++) {
                dist[i] = (long) (points[i][0] - right[0]) * (points[i][0] - right[0])
                        + (long) (points[i][1] - right[1]) * (points[i][1] - right[1]);
            }
            Arrays.sort(points, (s1, s2) -> {
                if (s1 == right) return -1;
                if (s2 == right) return 1;
                int ccw = ccw(s1, s2, right);
                if (ccw != 0) return ccw;
                return Long.compare(dist[s1[2]], dist[s2[2]]);
            });
            LinkedList<int[]> hull = new LinkedList<>();
            hull.add(points[0]);
            hull.add(points[1]);
            for (int s = 2; s < n; s++) {
                while (hull.size() > 1) {
                    int[] p2 = hull.pollLast();
                    int[] p1 = hull.getLast();
                    if (ccw(p2, points[s], p1) <= 0) {
                        hull.add(p2);
                        break;
                    }
                }
                hull.add(points[s]);
            }
            return hull.toArray(new int[0][]);
        }

        public static int[] v1(int[] i1, int[] i2) {
            return new int[]{i1[0] - i2[0], i1[1] - i2[1]};
        }

        private static int ccw(int[] s1, int[] s2, int[] right) {
            long xa = s1[0] - right[0];
            long xb = s1[1] - right[1];
            long ya = s2[0] - right[0];
            long yb = s2[1] - right[1];
            return Long.compare(xb * ya, xa * yb);
        }

        public static long dot(long[] v11, long[] v12) {
            return (long) v11[0] * v12[0] + (long) v11[1] * v12[1];
        }

        public static double f(long[] x) {
            return Math.sqrt(x[0] * x[0] + x[1] * x[1]);
        }

        public static double angle(int[] v1, int[] v2) {
            long[] v11 = new long[v1.length];
            long[] v12 = new long[v2.length];
            for (int s = 0; s < v1.length; s++) {
                v11[s] = v1[s];
            }
            for (int s = 0; s < v12.length; s++) {
                v12[s] = v2[s];
            }

            return Math.acos(dot(v11, v12) / f(v11) / f(v12));
        }

    }

    static class MyScan {
        BufferedReader br;
        StringTokenizer st;

        MyScan(BufferedReader br) {
            this.br = br;
        }

        public MyScan(InputStream in) {
            this(new BufferedReader(new InputStreamReader(in)));
        }

        public void findToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            findToken();
            return st.nextToken();
        }

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

    }
}