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.awt.geom.Line2D;
import java.util.Arrays;
import java.util.Comparator;

public class Main {


  private static void solve() {
    int n = ni();
    double[] x = new double[n];
    double[] y = new double[n];
    for (int i = 0; i < n; i ++) {
      x[i] = ni();
      y[i] = ni();
    }

    int[] ch = convexHull(x, y);
    int m = ch.length;
    double[] prob = new double[m];
    
    for (int i = 0; i < m; i ++) {
      int pre = (i + m - 1) % m;
      int next = (i + 1) % m;
      
      double dx1 = x[ch[pre]] - x[ch[i]];
      double dy1 = y[ch[pre]] - y[ch[i]];
      double dx2 = x[ch[next]] - x[ch[i]];
      double dy2 = y[ch[next]] - y[ch[i]];
      
      double a = Math.abs(Math.atan2(dy2, dx2) - Math.atan2(dy1, dx1));
      if (a < Math.PI) {
        a = 2 * Math.PI - a;
      }
      prob[i] = (a - Math.PI) / (2 * Math.PI);
    }
    double[] ans = new double[n];
    for (int i = 0; i < m; i ++) {
      ans[ch[i]] = prob[i];
    }
    for (double v : ans) {
      System.out.printf("%.12f\n", v);
    }
  }
  
  public static int[] convexHull(final double[] x, final double[] y)
  {
      int n = x.length;
      Integer[] ord = new Integer[n];
      for(int i = 0;i < n;i++)ord[i] = i;
      Arrays.sort(ord, new Comparator<Integer>(){
          public int compare(Integer a, Integer b){
              if(x[a] != x[b])return x[a] < x[b] ? -1 : 1;
              if(y[a] != y[b])return y[a] < y[b] ? -1 : 1;
              return 0;
          }
      });
      
      int[] ret = new int[n + 1];
      int p = 0;
      for(int i = 0;i < n;i++){
          if(p >= 1 && x[ret[p-1]] == x[ord[i]] && y[ret[p-1]] == y[ord[i]])continue;
          while(p >= 2 && Line2D.relativeCCW(
                  x[ret[p-2]], y[ret[p-2]],
                  x[ret[p-1]], y[ret[p-1]],
                  x[ord[i]], y[ord[i]]) == 1)p--;
          ret[p++] = ord[i];
      }
      
      int inf = p + 1;
      for(int i = n - 2;i >= 0;i--){
          if(x[ret[p-1]] == x[ord[i]] && y[ret[p-1]] == y[ord[i]])continue;
          while(p >= inf && Line2D.relativeCCW(
                  x[ret[p-2]], y[ret[p-2]],
                  x[ret[p-1]], y[ret[p-1]],
                  x[ord[i]], y[ord[i]]) == 1)p--;
          ret[p++] = ord[i];
      }
      
      return Arrays.copyOf(ret, p - 1);
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = System.getProperty("debug");
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static 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();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  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 char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}