python3 <<'PY'
import math
a=0.25; b=1.0/12
def Aval(y1,y2,q,r):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; nu1=a+b; q2=alpha-q
    if q<=0 or q2<=0: return -1
    lo=max(0.0,q-(alpha-mu1)); hi=min(q,mu1)
    if r<lo-1e-12 or r>hi+1e-12: 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
    return (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)))+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))))
def best2(y1,y2,N=500):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=alpha-mu1
    best=-1; arg=None
    for iq in range(1,N):
      q=alpha*iq/N
      lo=max(0.0,q-mu2); hi=min(q,mu1)
      for ir in range(N+1):
        r=lo+(hi-lo)*ir/N
        v=Aval(y1,y2,q,r)
        if v>best: best=v; arg=(q,r)
    return best,arg
def total(y1,y2,A):
    y3=a; gam=y1+y2+y3
    C=math.sqrt(gam)*(math.sqrt(b*y1)+math.sqrt(a*y2)+math.sqrt(a*y3))
    return A+b**1.5+C
for y1,y2 in [(b,0.0),(b,0.1),(b,0.2),(0.0,0.0),(0.0,a),(b,a),(0.04,0.0)]:
  A,arg=best2(y1,y2,300)
  print(y1,y2,"A",A,"tot",total(y1,y2,A),"arg",arg)
PY