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.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

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

    static class TaskC {
        static long MOD = 1_000_000_007;

        class Point implements Comparable<Point> {
            public double x, y;
            public int index;
            public Point ccwNeighbor;
            public Point cwNeighbor;
            double maxDegree;
            double minDegree;

            public void CalcMaxMin() {
                if (ccwNeighbor == null) {
                    maxDegree = 0;
                    minDegree = 0;
                } else {
                    maxDegree = (-Math.atan2(cwNeighbor.y - y, cwNeighbor.x - x) - Math.PI / 2) % (2 * Math.PI);
                    minDegree = (-Math.atan2(y - ccwNeighbor.y, x - ccwNeighbor.x) - Math.PI / 2) % (2 * Math.PI);
                    while (maxDegree < 0) maxDegree += 2 * Math.PI;
                    while (minDegree < 0) minDegree += 2 * Math.PI;
                    if (maxDegree < minDegree) maxDegree += 2 * Math.PI;
                }
            }


            public double Prop() {
                return (maxDegree - minDegree) / (2 * Math.PI);
            }

            public double Distance(Point p) {
                return (x - p.x) * (x - p.x) + (y - p.y) * (y - p.y);
            }

            @Override
            public int compareTo(Point o) {
                if (o.x == x) {
                    return Double.compare(y, o.y);
                }
                return Double.compare(x, o.x);
            }
        }

        public void Solve(InputReader in, PrintWriter out) {
            int n = in.NextInt();
            Point[] ps = new Point[n];
            for (int i = 0; i < n; i++) {
                Point p = new Point();
                p.x = in.NextDouble();
                p.y = in.NextDouble();
                p.index = i;
                ps[i] = p;
            }
            if (n == 1) {
                out.println(1);
                return;
            }
            if (n == 2) {
                out.println(0.5);
                out.println(0.5);
                return;
            }
            Point min = ps[0];
            for (int i = 0; i < n; i++) {
                if (ps[i].compareTo(min) < 0) {
                    min = ps[i];
                }
            }
            Point first = min;
            while (true) {
                if (min.cwNeighbor != null) break;
                for (int i = 0; i < n; i++) {
                    if (min.compareTo(ps[i]) < 0) {
                        if (min.cwNeighbor == null) min.cwNeighbor = ps[i];
                        else {
                            double orentation = Orentation(min, min.cwNeighbor, ps[i]);
                            if (orentation == 0) {
                                if (min.cwNeighbor.compareTo(ps[i]) < 0) {
                                    min.cwNeighbor = ps[i];
                                }
                            }
                            if (orentation > 0) {
                                min.cwNeighbor = ps[i];
                            }
                        }
                    }
                }
                if (min.cwNeighbor != null) {
                    min.cwNeighbor.ccwNeighbor = min;
                    min = min.cwNeighbor;
                } else {
                    break;
                }
            }
            while (true) {
                if (min.cwNeighbor != null) break;
                for (int i = 0; i < n; i++) {
                    if (min.compareTo(ps[i]) > 0) {
                        if (min.cwNeighbor == null) min.cwNeighbor = ps[i];
                        else {
                            double orentation = Orentation(min, min.cwNeighbor, ps[i]);
                            if (orentation == 0) {
                                if (min.cwNeighbor.compareTo(ps[i]) > 0) {
                                    min.cwNeighbor = ps[i];
                                }
                            }
                            if (orentation > 0) {
                                min.cwNeighbor = ps[i];
                            }
                        }
                    }
                }
                if (min.cwNeighbor != null && min != first) {
                    min.cwNeighbor.ccwNeighbor = min;
                    min = min.cwNeighbor;
                } else {
                    break;
                }
            }


            for (Point p : ps) p.CalcMaxMin();
            for (Point p : ps) out.println(p.Prop());

        }

        public double Orentation(Point a, Point b, Point c) {
            return ((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x));

        }
    }


    public static int GetMax(int[] ar) {
        int max = Integer.MIN_VALUE;
        for (int a : ar) {
            max = Math.max(max, a);
        }
        return max;
    }

    public static int GetMin(int[] ar) {
        int min = Integer.MAX_VALUE;
        for (int a : ar) {
            min = Math.min(min, a);
        }
        return min;
    }

    public static long GetSum(int[] ar) {
        long s = 0;
        for (int a : ar) s += a;
        return s;
    }

    public static int[] GetCount(int[] ar) {
        return GetCount(ar, GetMax(ar));
    }

    public static int[] GetCount(int[] ar, int maxValue) {
        int[] dp = new int[maxValue + 1];
        for (int a : ar) {
            dp[a]++;
        }
        return dp;
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String Next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine(), " \t\n\r\f,");
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int NextInt() {
            return Integer.parseInt(Next());
        }

        public long NextLong() {
            return Long.parseLong(Next());
        }

        public double NextDouble() {
            return Double.parseDouble(Next());
        }

        public int[] NextIntArray(int n) {
            return NextIntArray(n, 0);
        }

        public int[] NextIntArray(int n, int offset) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = NextInt() - offset;
            }
            return a;
        }

        public int[][] NextIntMatrix(int n, int m) {
            return NextIntMatrix(n, m, 0);
        }

        public int[][] NextIntMatrix(int n, int m, int offset) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = NextInt() - offset;
                }
            }
            return a;
        }
    }
}