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(20):
      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 p_row2(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>mu2+1e-12 or mu1<1e-12: return -1
    c=nu1-a*q2/mu1
    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; z2=mu2-q
    return math.sqrt(max(0,b*q*c))+math.sqrt(max(0,a*q*(q-c)))+math.sqrt(max(0,a*x2*c2))+math.sqrt(max(0,b*x2*(q2-c2)))+math.sqrt(max(0,b*z2*c2))+math.sqrt(max(0,a*z2*(q2-c2)))
def p_col1(y1,y2,q):
    al=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2; nu1=a+b
    if q<=0 or q>=nu1: return -1
    q2=al-q; nu3=al-nu1
    den=nu3
    r=(a*q2-mu1*(nu1-q))/den
    if r<-1e-10 or r>q+1e-10: return -1
    c2=nu1-q; x2=mu1-r; z2=mu2-(q-r)
    return math.sqrt(max(0,a*q*r))+math.sqrt(max(0,b*q*(q-r)))+math.sqrt(max(0,a*x2*c2))+math.sqrt(max(0,b*x2*nu3))+math.sqrt(max(0,b*z2*c2))+math.sqrt(max(0,a*z2*nu3))
def p_col3(y1,y2,q):
    al=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2; nu1=a+b; nu3=al-nu1
    if q<=0 or q>nu3+1e-12 or nu1<1e-12: return -1
    q2=al-q
    r=mu1-a*q2/nu1
    if r<-1e-10 or r>q+1e-10: return -1
    x2=mu1-r; z2=mu2-(q-r); c3=nu3-q
    return math.sqrt(max(0,b*q*r))+math.sqrt(max(0,a*q*(q-r)))+math.sqrt(max(0,a*x2*nu1))+math.sqrt(max(0,b*x2*c3))+math.sqrt(max(0,b*z2*nu1))+math.sqrt(max(0,a*z2*c3))
for name,fn,qf in [("row2",p_row2,"mu2"),("col1",p_col1,"nu1"),("col3",p_col3,"nu3")]:
  best=-1; arg=None
  for _ in range(25000):
    y1=random.random()*b; y2=random.random()*a
    al=2*a+2*b-y1-y2; mu2=b+a-y2; nu1=a+b; nu3=al-nu1
    mx={"mu2":mu2,"nu1":nu1,"nu3":nu3}[qf]
    q=random.uniform(1e-9,max(1e-9,mx))
    A=fn(y1,y2,q)
    if A<0: continue
    tot=A+BC(y1,y2)
    if tot>best: best=tot; arg=(y1,y2,q,A,tot)
  print(name,best,arg)
PY