#!/usr/bin/env python
import math

class Ellipse:
 def __init__(self, x,y, rx,ry):
  self.x  = x
  self.y  = y
  self.rx = rx
  self.ry = ry

class Matrix:
 def __init__(self, ellipse):
  self.half_width  = max(int(math.ceil(ellipse.rx + ellipse.x) + 1),
                         int(math.ceil(ellipse.ry + ellipse.y) + 1))
  self.half_height = self.half_width
  self.width       = self.half_width * 2
  self.height      = self.half_height * 2
  self.cells       = [[0 for x in range(self.width)] for y in range(self.height)]
 def display(self):
  codes = '0123456789abcdefghijklmnopqrstuvwxyz'
  print('\n'.join([''.join([codes[self.cells[y][x]] for x in range(self.width)])
                                                    for y in range(self.height)]))
 def draw_ellipse(self, i_bit, ellipse, angle):
  mask_bit  = (1 << i_bit)
  sin_angle = math.sin(math.radians(angle))
  cos_angle = math.cos(math.radians(angle))
  for matrix_y in range(self.height):
   for matrix_x in range(self.width):
    cell_x_unrotated = matrix_x - self.half_width
    cell_y_unrotated = matrix_y - self.half_height
    cell_x = sin_angle * cell_y_unrotated + cos_angle * cell_x_unrotated
    cell_y = cos_angle * cell_y_unrotated - sin_angle * cell_x_unrotated
    cell_dx = float(cell_x - ellipse.x) / ellipse.rx
    cell_dy = float(cell_y - ellipse.y) / ellipse.ry
    # print('%3d%3d | %4d%4d | %6.2f%6.2f | %6.2f %d' %
    #       (matrix_x,matrix_y, cell_x,cell_y, cell_dx,cell_dy,
    #        cell_dx * cell_dx + cell_dy * cell_dy,cell_dx * cell_dx + cell_dy * cell_dy > 1))
    if (cell_dx * cell_dx + cell_dy * cell_dy <= 1): self.cells[matrix_y][matrix_x] |= mask_bit
 def draw_ellipses(self, ellipse):
  for i_ellipse in range(5): self.draw_ellipse(i_ellipse, ellipse, i_ellipse * 72)
 def count_regions(self):
  counts = [0 for code in range(1 << 5)]
  for matrix_y in range(self.height):
   for matrix_x in range(self.width):
    counts[self.cells[matrix_y][matrix_x]] += 1
  area_all  = self.width * self.height
  area_min  = area_all
  area_non0 = area_all - counts[0]
  for i_count in range(len(counts)):
   if (area_min > counts[i_count]): area_min = counts[i_count]
  if (True):
   # if (area_min > 0):
    bar = ''.join(['%-5d+----' % i for i in range(99)]).replace(' ','-')[1:]
    ppm = 1e6 * area_min / area_non0
    print('x:%2d y:%2d rx:%2d ry:%2d ppm:%4.0f %s' %
          (ellipse.x,ellipse.y, ellipse.rx,ellipse.ry, ppm, bar[:int(ppm / 100 + 0.5)]))
"""
ellipse = Ellipse(9,14, 40,80)
ellipse = Ellipse(7,16, 42,78)
ellipse = Ellipse(5,12, 46,70)
ellipse = Ellipse(5,14, 37,64)
ellipse = Ellipse(5,12, 40,65)
ellipse = Ellipse(5,12, 41,66)
ellipse = Ellipse(10,24, 82,132)
matrix  = Matrix(ellipse)
matrix.draw_ellipses(ellipse)
matrix.display()
matrix.count_regions()
"""
model_x  =  20; half_range_x  = 1; step_x  = 1
model_y  =  46; half_range_y  = 1; step_y  = 1
model_rx = 166; half_range_rx = 1; step_rx = 1
model_ry = 264; half_range_ry = 1; step_ry = 1
for    x  in range(-half_range_x , half_range_x  + 1, step_x ):
 for   y  in range(-half_range_y , half_range_y  + 1, step_y ):
  for  rx in range(-half_range_rx, half_range_rx + 1, step_rx):
   for ry in range(-half_range_ry, half_range_ry + 1, step_ry):
    ellipse = Ellipse(model_x + x,model_y + y, model_rx + rx,model_ry + ry)
    matrix  = Matrix(ellipse)
    matrix.draw_ellipses(ellipse)
    matrix.count_regions()
# """