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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		int[][] co = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = new int[]{ni(), ni()};
		}
		boolean[] dead = new boolean[n];
		outer:
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				for(int k = j+1;k < n;k++){
					if(j == i || k == i)continue;
					if(isACB(co[j][0], co[j][1], 
							co[k][0], co[k][1],
							co[i][0], co[i][1])){
						dead[i] = true;
						continue outer;
					}
					
					for(int l = k+1;l < n;l++){
						if(j == i || k == i || l == i)continue;
						if(onSameLine(co[j], co[k], co[l]))continue;
						int c1 = ccw(co[j], co[k], co[i]);
						int c2 = ccw(co[k], co[l], co[i]);
						int c3 = ccw(co[l], co[j], co[i]);
						if(c1+c2+c3 == 3 || c1+c2+c3 == -3){
							dead[i] = true;
							continue outer;
						}
					}
				}
			}
		}
		
		int alive = 0;
		for(int i = 0;i < n;i++){
			if(!dead[i])alive++;
		}
		if(alive == 2){
			for(int i = 0;i < n;i++){
				if(dead[i]){
					out.println(0);
				}else{
					out.println(0.5);
				}
			}
			return;
		}
		
		outer:
		for(int i = 0;i < n;i++){
			if(dead[i]){
				out.println(0);
				continue;
			}
			
			double[][] theta = new double[n-1][];
			int p = 0;
			for(int j = 0;j < n;j++){
				if(j == i)continue;
				theta[p++] = new double[]{Math.atan2(
						co[j][1]-co[i][1], 
						co[j][0]-co[i][0]
								), j};
			}
			Arrays.sort(theta, new Comparator<double[]>() {
				public int compare(double[] a, double[] b) {
					return Double.compare(a[0], b[0]);
				}
			});
			for(int j = 0;j < n-1;j++){
				int cur = (int)theta[j][1];
				int nex = (int)theta[(j+1)%(n-1)][1];
				if(inArg(
						co[cur][0]-co[i][0],
						co[cur][1]-co[i][1],
						-(co[cur][0]-co[i][0]),
						-(co[cur][1]-co[i][1]),
						co[nex][0]-co[i][0],
						co[nex][1]-co[i][1]) < 0){
//					tr(cur, i, nex);
					double val = Math.atan2(
							co[nex][1]-co[i][1], 
							co[nex][0]-co[i][0]
									) - Math.atan2(
											co[cur][1]-co[i][1], 
											co[cur][0]-co[i][0]
													) - Math.PI;
					if(val < -1e-5)val += 2*Math.PI;
					out.printf("%.14f\n", val/(2*Math.PI));
					continue outer;
				}
			}
		}
	}
	public static boolean onSameLine(int[] a, int[] b, int[] c)
	{
		return (long)(c[0]-a[0])*(b[1]-a[1])-(long)(c[1]-a[1])*(b[0]-a[0])==0;
	}

	
	public static boolean isACB(long ax, long ay, long bx, long by, long cx, long cy)
	{
		return (cx-ax)*(by-ay)-(cy-ay)*(bx-ax)==0 && (cx-ax)*(cx-bx)+(cy-ay)*(cy-by) <= 0;
	}
	
	public static int inArg(long ax, long ay, long bx, long by, long cx, long cy)
	{
		return (int)(Long.signum(ax*cy-ay*cx)-Long.signum(bx*cy-by*cx)-Long.signum(ax*by-ay*bx));
	}

	
	public static int ccw(int[] a, int[] b, int[] t){ return Long.signum((long)(t[0]-a[0])*(b[1]-a[1])-(long)(b[0]-a[0])*(t[1]-a[1])); }

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static 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 static 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 static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static 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 static 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) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}