#!/usr/bin/env python3
import math,random
W,H=140,110
pos=[(x,y) for y in range(0,H+1,5) for x in range(0,W+1,5)]
def cmask(x,y,r):
 z=0
 for j in range(H):
  dy=j+.5-y;t=r*r-dy*dy
  if t>=0:
   d=math.sqrt(t);l=max(0,math.ceil(x-d-.5));u=min(W-1,math.floor(x+d-.5))
   if u>=l:z|=((1<<(u-l+1))-1)<<(j*W+l)
 return z
def smask(x,y):
 z=0;l=max(0,math.ceil(x-5.5));u=min(W-1,math.floor(x+4.5))
 for j in range(H):
  if abs(j+.5-y)<=5 and u>=l:z|=((1<<(u-l+1))-1)<<(j*W+l)
 return z
M=[[cmask(x,y,20) for x,y in pos],[cmask(x,y,5) for x,y in pos],[smask(x,y) for x,y in pos]]
pc=lambda z:bin(z).count('1')
def run(types,seed):
 random.seed(seed);s=[];u=0
 for t in types:
  v=sorted((pc(u|m),i) for i,m in enumerate(M[t]))
  q=1 if seed==0 else min(15,len(v));_,i=random.choice(v[-q:]);s.append((t,i));u|=M[t][i]
 cur=pc(u)
 for sweep in range(2):
  order=list(range(len(s)));random.shuffle(order)
  for q in order:
   base=0
   for k,(t,i) in enumerate(s):
    if k!=q:base|=M[t][i]
   t=s[q][0];v,i=max((pc(base|m),i) for i,m in enumerate(M[t]))
   if v>cur:s[q]=(t,i);cur=v
 return cur,s
n2,n1,nr=8,0,42
types=[0]*n2+[2]*nr+[1]*n1
best=max(run(types,q) for q in range(2))
print('RESULT',best[0],best[0]/15400,20000*n2+1600*n1+2000*nr)
print([(t,pos[i]) for t,i in best[1]])