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.*;

class Solver {
  int n;
  double[] x;
  double[] y;
  
  public double[] solve(int n, double[] x, double[] y) {
    this.n = n;
    this.x = x;
    this.y = y;
    
    ArrayList<Double> atanList = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      for (int j = i+1; j < n; j++) {
        double a1 = Math.atan2(y[j] - y[i], x[j] - x[i]) + Math.PI / 2;
        if (a1 < 0) {
          a1 += 2.0 * Math.PI;
        }
        
        atanList.add(a1);
        if (a1 < Math.PI) {
          atanList.add(a1 + Math.PI);
        } else {
          atanList.add(a1 - Math.PI);
        }
      }
    }
    
    atanList.add(0.0);
    atanList.add(2.0 * Math.PI);
    
    Collections.sort(atanList);
    
    double[] answer = new double[n];
    for (int i = 1; i < atanList.size(); i++) {
      double width = atanList.get(i) - atanList.get(i - 1);
      double mid = (atanList.get(i) + atanList.get(i - 1)) / 2;
      
      double infX = 1e12 * Math.cos(mid);
      double infY = 1e12 * Math.sin(mid);
      
      double minD = Math.hypot(infX - x[0], infY - y[0]);
      int minIndex = 0;
      for (int j = 1; j < n; j++) {
        double d = Math.hypot(infX - x[j], infY - y[j]);
        if (d < minD) {
          minD = d;
          minIndex = j;
        }
      }
      
      answer[minIndex] += width / 2.0 / Math.PI;
    }
    return answer;
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int n = reader.nextInt();
    double[] x = new double[n];
    double[] y = new double[n];
    for (int i = 0; i < n; i++) {
      x[i] = reader.nextDouble();
      y[i] = reader.nextDouble();
    }
    double[] answer = new Solver().solve(n, x, y);
    for (double d : answer) {
      out.printf("%.20f\n", d);
    }
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception 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) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLongArray(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
}

class Algorithm {
  private static void swap(Object[] list, int a, int b) {
    Object tmp = list[a];
    list[a] = list[b];
    list[b] = tmp;
  }
  
  public static <T extends Comparable<? super T>> boolean nextPermutation(T[] ts) {
    int rightMostAscendingOrderIndex = ts.length - 2;
    while (rightMostAscendingOrderIndex >= 0 &&
        ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostAscendingOrderIndex + 1]) >= 0) {
      rightMostAscendingOrderIndex--;
    }
    if (rightMostAscendingOrderIndex < 0) {
      return false;
    }
    
    int rightMostGreatorIndex = ts.length - 1;
    while (ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostGreatorIndex]) >= 0) {
      rightMostGreatorIndex--;
    }
    
    swap(ts, rightMostAscendingOrderIndex, rightMostGreatorIndex);
    for (int i = 0; i < (ts.length - rightMostAscendingOrderIndex - 1) / 2; i++) {
      swap(ts, rightMostAscendingOrderIndex + 1 + i, ts.length - 1 - i);
    }
    return true;
  }
}