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: Accepted)

import java.io.*;
import java.util.*;


public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();

        List<Pair> xy = new ArrayList<>();
        for (int i = 0; i < n; i++) {
        	xy.add(new Pair(sc.nextInt(), sc.nextInt(), i));
        }
        Collections.sort(xy);

        List<Pair> ch = new ArrayList<>();

        for (int i = 0; i < xy.size(); i++) {
        	while (ch.size() > 1
        			&& (Geom.cross(ch.get(ch.size() - 1).a - ch.get(ch.size() - 2).a, ch.get(ch.size() - 1).b - ch.get(ch.size() - 2).b, xy.get(i).a - ch.get(ch.size() - 1).a, xy.get(i).b - ch.get(ch.size() - 1).b)) <= 0) {
        		ch.remove(ch.size() - 1);
        	}
        	ch.add(xy.get(i));
        }
        int t = ch.size();
        for (int i = xy.size() - 1; i >= 0; i--) {
        	while (ch.size() > t
        			&& (Geom.cross(ch.get(ch.size() - 1).a - ch.get(ch.size() - 2).a, ch.get(ch.size() - 1).b - ch.get(ch.size() - 2).b, xy.get(i).a - ch.get(ch.size() - 1).a, xy.get(i).b - ch.get(ch.size() - 1).b)) <= 0) {
        		ch.remove(ch.size() - 1);
        	}
        	ch.add(xy.get(i));
        }

        ch.remove(ch.size() - 1);

        List<Double> the = new ArrayList<>();
        for (int i = 0, size = ch.size(); i < size; i++) {
        	double x1 = ch.get(i).a;
        	double y1 = ch.get(i).b;
        	double x2 = ch.get((i + 1) % size).a;
        	double y2 = ch.get((i + 1) % size).b;

        	double tmp = Math.atan2(y2 - y1, x2 - x1);
//        	tmp -= Math.PI / 2;
//        	if (tmp < -Math.PI) {
//        		tmp += 2 * Math.PI;
//        	}

        	the.add(tmp);
        }

        /*
        double sum = 0;
        for (int i = 0, size = ch.size(); i < size; i++) {
        	double tmp = the.get((i + 1) % size) - the.get(i);
        	if (tmp < 0) {
        		tmp += 2 * Math.PI;
        	}

        	sum += tmp;
        }

        pr.println(sum);
        pr.println(sum / 2 / Math.PI);
        */

        double[] ans = new double[n];
        for (int i = 0, size = ch.size(); i < size; i++) {
        	double tmp = the.get((i + 1) % size) - the.get(i);
        	tmp += 2 * Math.PI;
        	tmp %= 2 * Math.PI;

        	ans[ch.get((i + 1) % size).c] = tmp;
        }

        for (int i = 0; i < n; i++) {
        	pr.printf("%.6f\n", ans[i] / 2 / Math.PI);
        }
    }

    private static class Pair implements Comparable<Pair> {
    	int a;
    	int b;
    	int c;

    	Pair(int a, int b, int c) {
    		this.a = a;
    		this.b = b;
    		this.c = c;
    	}

		@Override
		public int compareTo(Pair o) {
			if (this.a == o.a) {
				return Integer.compare(this.b, o.b);
			}

			return Integer.compare(this.a, o.a);
		}

		@Override
		public String toString() {
			return "[" + Integer.toString(a) + " " + Integer.toString(b) + "]";
		}
    }

	private static class Geom {
		static long cross(int xa, int ya, int xb, int yb) {
			return (long)xa * yb - (long)xb * ya;
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);

		solve();

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}