python3 <<'PY'
import math,random
a=0.25; b=1.0/12
def BC(y1,y2):
    lo=0.0; hi=a; gr=(math.sqrt(5)-1)/2
    def f(y3):
      beta=a+b-y3; B=math.sqrt(beta)*(b+math.sqrt(max(0,a*(a-y3))))
      gam=y1+y2+y3; C=math.sqrt(gam)*(math.sqrt(max(0,b*y1))+math.sqrt(max(0,a*y2))+math.sqrt(max(0,a*y3)))
      return B+C
    for _ in range(25):
      c=hi-gr*(hi-lo); d=lo+gr*(hi-lo)
      if f(c)<f(d): lo=c
      else: hi=d
    return f((lo+hi)/2)
def pure_row1(y1,y2,q):
    al=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2; nu1=a+b; q2=al-q
    if q<=0 or q2<=0 or q>mu1+1e-12: return -1
    c=(a*q2-(mu1-q)*nu1)/mu2
    if c<-1e-10 or c>q+1e-10 or c>nu1+1e-10 or nu1-c>q2+1e-10: return -1
    c2=nu1-c; x2=mu1-q
    return math.sqrt(a*q*c)+math.sqrt(max(0,b*q*(q-c)))+math.sqrt(max(0,a*x2*c2))+math.sqrt(max(0,b*x2*(q2-c2)))+math.sqrt(max(0,b*mu2*c2))+math.sqrt(max(0,a*mu2*(q2-c2)))
best=-1; arg=None
for _ in range(30000):
  y1=random.random()*b; y2=random.random()*a
  al=2*a+2*b-y1-y2; mu1=a+b-y1
  q=random.uniform(1e-9,mu1)
  A=pure_row1(y1,y2,q)
  if A<0: continue
  tot=A+BC(y1,y2)
  if tot>best: best=tot; arg=(y1,y2,q,A,tot)
print("best",best,arg,"1-best",1-best)
PY