python3 <<'PY'
import math,random
a=0.25; b=1.0/12
def G(y1,y2,q,r):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2; nu1=a+b
    q2=alpha-q
    if y1<0 or y1>b or y2<0 or y2>a or q<=1e-12 or q2<=1e-12: return -1
    lo=max(0.0,q-mu2); hi=min(q,mu1)
    if r<lo-1e-11 or r>hi+1e-11: return -1
    den=r*q2/q-(mu1-r)
    if abs(den)<1e-14: return -1
    c=(a*q2-(mu1-r)*nu1)/den
    if c<-1e-10 or c>q+1e-10 or c>nu1+1e-10 or nu1-c>q2+1e-10: return -1
    r2=mu1-r; c2=nu1-c
    t1=math.sqrt(max(0,a*r*c))+math.sqrt(max(0,b*r*(q-c)))+math.sqrt(max(0,b*(q-r)*c))+math.sqrt(max(0,a*(q-r)*(q-c)))
    t2=math.sqrt(max(0,a*r2*c2))+math.sqrt(max(0,b*r2*(q2-c2)))+math.sqrt(max(0,b*(q2-r2)*c2))+math.sqrt(max(0,a*(q2-r2)*(q2-c2)))
    C=math.sqrt(y1+y2+a)*(math.sqrt(b*y1)+math.sqrt(a*y2)+a)
    return t1+t2+b**1.5+C
best=-1; arg=None
for it in range(1000000):
  y1=random.random()*b; y2=random.random()*a
  alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2
  q=random.uniform(1e-10,alpha-1e-10)
  lo=max(0.0,q-mu2); hi=min(q,mu1)
  if hi<lo: continue
  r=random.uniform(lo,hi)
  g=G(y1,y2,q,r)
  if g>best: best=g; arg=(y1,y2,q,r)
print("best",best,arg,"cost",1-best)
PY