Problem:
Score : 600 points

Problem Statement

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}.

Sample Input 1

2
0 0
1 1

Sample Output 1

0.5
0.5

If Ringo put Snuke in the region x+y\leq 1, Snuke will fall into the first hole. The probability of this happening is very close to 0.5.
Otherwise, Snuke will fall into the second hole, the probability of which happening is also very close to 0.5.

Sample Input 2

5
0 0
2 8
4 5
2 6
3 10

Sample Output 2

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.*;

public class Main implements Runnable {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
    }

    public void run() {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int n = in.nextInt();
        List<int[]> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int[] p = {in.nextInt(), in.nextInt(), i};
            list.add(p);
        }
        // ch.get(last) contains first
        List<int[]> ch = convexHull(list);
        double[] ans = new double[n];

        for (int i = 0; i < ch.size(); i++) {
            int[] p = ch.get(i);
            int[] pre = ch.get((i - 1 + ch.size()) % ch.size());
            int[] post = ch.get((i + 1 + ch.size()) % ch.size());
            int x1 = pre[0] - p[0];
            int y1 = pre[1] - p[1];
            int x2 = post[0] - p[0];
            int y2 = post[1] - p[1];
            double a = angle(x1, y1, x2, y2);
            ans[p[2]] = (Math.PI - a) / (Math.PI * 2);
        }
        for (int i = 0; i < n; i++) {
            System.out.println(ans[i]);
        }
    }

    public static List<int[]> convexHull(List<int[]> list){
        int k = 0;
        Collections.sort(list, new Comparator<int[]>(){
            @Override
            public int compare(int[] o1, int[] o2) {
                if(o1[0] != o2[0]) return o1[0]-o2[0];
                return o1[1]-o2[1];
            }
        });
        int n = list.size();
        int[][] qs = new int[n*2][2];
        for(int i=0; i<n; i++){
            while(k > 1 && cross(qs[k-2], qs[k-1], qs[k-1], list.get(i)) < 0) k--;
            qs[k++] = list.get(i);
        }

        for(int i=n-2, t=k; i>=0; i--){
            while(k > t && cross(qs[k-2], qs[k-1], qs[k-1], list.get(i)) < 0) k--;
            qs[k++] = list.get(i);
        }

        List<int[]> res = new ArrayList<>();
        for(int i=0; i<k-1; i++){
            res.add(qs[i]);
        }
        return res;
    }

    public static int cross(int[] p11, int[] p12, int[] p21, int[] p22){
        return (p12[0]-p11[0])*(p22[1]-p21[1]) - (p22[0]-p21[0])*(p12[1]-p11[1]);
    }

    double angle(double x1, double y1, double x2, double y2){
        double a1 = Math.atan2(y1, x1);
        double a2 = Math.atan2(y2, x2);
        double rad = Math.abs(a1-a2);
        if(rad>Math.PI) rad = 2*Math.PI - rad;
        return rad;
    }
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
    @Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
    public void add(T key,int v){put(key,get(key)+v);}
    public void add(T key){put(key,get(key)+1);}
    public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
    public MultiSet<T> merge(MultiSet<T> set)
    {MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
        for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}

class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}