python3 <<'PY'
import math,random
a=0.25; b=1.0/12
def bestK(y1,y2,K=4,N=200000):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; nu1=a+b
    best=-1
    for _ in range(N):
      w=[random.random() for i in range(K)]; sw=sum(w); q=[alpha*v/sw for v in w]
      u=[random.random() for i in range(K)]; su=sum(u); aa=[mu1*v/su for v in u]
      if any(aa[i]>q[i]+1e-12 for i in range(K)): continue
      cc=[0.0]*K
      rem=nu1
      for i in range(K-1):
        maxc=min(q[i],rem)
        ci=random.random()*maxc
        cc[i]=ci; rem-=ci
      a4=aa[K-1]; q4=q[K-1]
      if a4<1e-14: continue
      target=a
      for i in range(K-1):
        target-=aa[i]*cc[i]/q[i]
      c4=target*q4/a4
      if c4<-1e-10 or c4>q4+1e-10: continue
      cc[K-1]=c4
      if abs(sum(cc)-nu1)>1e-9: continue
      val=0.0
      for i in range(K):
        qi=q[i]; ai=aa[i]; ci=cc[i]
        bi=qi-ai; di=qi-ci
        val+=math.sqrt(max(0,a*ai*ci))+math.sqrt(max(0,b*ai*di))+math.sqrt(max(0,b*bi*ci))+math.sqrt(max(0,a*bi*di))
      if val>best: best=val
    return best
for y1,y2 in [(0.035,0.095),(0.02,0.22),(0.0,0.0)]:
  print(y1,y2,bestK(y1,y2,4,200000))
PY