#!/usr/bin/env python3
import math,random
h=.5;W,H=int(140/h),int(110/h)
pos=[(x,y) for y in range(0,111,5) for x in range(0,141,5)]
def circle(x,y,r):
 z=0
 for j in range(H):
  b=(j+.5)*h;q=r*r-(b-y)**2
  if q>=0:
   d=math.sqrt(q);l=max(0,math.ceil((x-d)/h-.5));u=min(W-1,math.floor((x+d)/h-.5))
   if u>=l:z|=((1<<(u-l+1))-1)<<(j*W+l)
 return z
def square(x,y):
 z=0;l=max(0,math.ceil((x-5)/h-.5));u=min(W-1,math.floor((x+5)/h-.5))
 for j in range(H):
  b=(j+.5)*h
  if abs(b-y)<=5 and u>=l:z|=((1<<(u-l+1))-1)<<(j*W+l)
 return z
M=[[circle(x,y,20) for x,y in pos],[circle(x,y,5) for x,y in pos],[square(x,y) for x,y in pos]]
idx={p:i for i,p in enumerate(pos)}
c2=[(50,20),(125,90),(110,55),(70,55),(90,90),(90,20),(20,90),(30,55),(15,20),(125,20),(55,90)]
c1=[(135,50),(5,70),(5,55),(5,45)];squares=[(135,60)]
s=[(0,idx[p]) for p in c2]+[(1,idx[p]) for p in c1]+[(2,idx[p]) for p in squares]
def uni(ss):
 u=0
 for t,i in ss:u|=M[t][i]
 return u
cur=uni(s).bit_count();print('start',cur*h*h)
for sweep in range(6):
 imp=0
 for q in range(len(s)):
  base=uni(s[:q]+s[q+1:]);t=s[q][0]
  v,i=max(((base|m).bit_count(),i) for i,m in enumerate(M[t]))
  if v>cur:s[q]=(t,i);cur=v;imp+=1
 print('sweep',sweep,cur*h*h,imp)
 if not imp:break
print([(t,pos[i]) for t,i in s])