output_description: 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}.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      x_1 y_1
      :
      x_N y_N
attempt: #! /usr/bin/env python
  # -*- coding: utf-8 -*-
  # vim:fenc=utf-8
  #
  
  """
  AGC021 B
  """
  
  import math
  from collections import defaultdict
  
  n = int(input())
  ps = [tuple(map(int, input().split())) for i in range(n)]
  
  
  def dist(rad, p):
      radtmp = 2 * math.pi * rad / maxcut
      return -p[0] * math.cos(radtmp) - p[1] * math.sin(radtmp)
  
  
  def closest(rad):
      tmp = dist(rad, ps[0])
      itmp = 0
      for i, pp in enumerate(ps):
          tmp2 = dist(rad, pp)
          if tmp2 < tmp:
              itmp = i
              tmp = tmp2
      return itmp
  
  
  maxcut = 2**20
  
  
  binary = defaultdict(int)
  binary[0] = closest(0)
  binary[maxcut] = binary[0]
  binary[maxcut // 2] = closest(maxcut // 2)
  binary[maxcut // 4] = closest(maxcut // 4)
  binary[3 * maxcut // 4] = closest(3 * maxcut // 4)
  
  
  def fillbinary(ll, rr):
      if binary[ll] != binary[rr] and rr - ll != 1:
          mm = (ll + rr) // 2
          binary[mm] = closest(mm)
          fillbinary(ll, mm)
          fillbinary(mm, rr)
  
  
  fillbinary(0, maxcut // 4)
  fillbinary(maxcut // 4, maxcut // 2)
  fillbinary(maxcut // 2, 3 * maxcut // 4)
  fillbinary(3 * maxcut // 4, maxcut)
  
  
  binkeys = sorted(binary.keys())
  ansli = [0] * n
  beforekey = 0
  for i in binkeys:
      ansli[binary[i]] += i - beforekey
      beforekey = i
  
  
  for i in range(n):
      print(ansli[i] / maxcut)
  
problem_description: 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.
samples: [{"input": "2\n    0 0\n    1 1", "output": "0.5\n    0.5\n    \n\nIf Ringo put Snuke in the region x+y\\leq 1, Snuke will fall into the first\nhole. The probability of this happening is very close to 0.5. Otherwise, Snuke\nwill fall into the second hole, the probability of which happening is also\nvery close to 0.5.\n\n* * *"}, {"input": "5\n    0 0\n    2 8\n    4 5\n    2 6\n    3 10", "output": "0.43160120892732328768\n    0.03480224363653196956\n    0.13880483535586193855\n    0.00000000000000000000\n    0.39479171208028279727"}]