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.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main{
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    int mod = 1_000_000_007;
    long inf = Long.MAX_VALUE;

    void solve(){
        int n = ni();
        long[] x = new long[n];
        long[] y = new long[n];
        List<long[]> list = new ArrayList<>();
        for(int i = 0; i < n; i++){
            x[i] = nl();
            y[i] = nl();
            list.add(new long[]{x[i], y[i], i});
        }
        double[] ans = new double[n];
        List<long[]> ch = convexHull(list);
        for(int i = 0; i < ch.size(); i++){
            long[] p = ch.get(i);
            long[] pre = ch.get((i-1+ch.size())%ch.size());
            long[] nex = ch.get((i+1+ch.size())%ch.size());
            long x1 = pre[0]-p[0];
            long y1 = pre[1]-p[1];
            long x2 = nex[0]-p[0];
            long y2 = nex[1]-p[1];
            double a = angle(x1,y1,x2,y2);
            ans[(int)p[2]] += (Math.PI - a) / (Math.PI * 2); 
        }
        for(int i = 0; i < n; i++){
            out.println(ans[i]);
        }
    } 

    public static List<long[]> convexHull(List<long[]> list){
        int k = 0;
        Collections.sort(list, new Comparator<long[]>(){
            @Override
            public int compare(long[] o1, long[] o2) {
                if(o1[0] != o2[0]) return Long.compare(o1[0], o2[0]);//o1[0]-o2[0];
                return Long.compare(o1[1], o2[1]);//o1[1]-o2[1];
            }
        });
        int n = list.size();
        long[][] qs = new long[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<long[]> res = new ArrayList<>();
        for(int i=0; i<k-1; i++){
            res.add(qs[i]);
        }
        return res;
    }
 
    public static long cross(long[] p11, long[] p12, long[] p21, long[] 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;
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}