python3 <<'EOF'
from fractions import Fraction as F
r=F('0.78')
u=F('0.05')
b=2-r
xm=2/b
q=F('-173/6000')
prev='I'
h=0
def cl(x,a,c):
    return a if x<a else (c if x>c else x)
def RF(x):
    z=(1-x)/b
    return z if z>0 else F(0)
def U(x):
    z=RF(x)
    return x-x*z-b/2*x*x
def PH(x):
    z=RF(x)
    z=(1-z)/b
    return z if z>0 else F(0)
C=[F(1)/(3-r)]
cm=F(1)/(3-r)
Uv=[U(c) for c in C]
def CL(x):
    ux=U(x)
    ph=PH(x)
    for i,c in enumerate(C):
        if ux>=Uv[i] and (ph-x)*(c-x)>=0:
            return 1
    mn=min(Uv)
    if ux>=mn and C[0]<=x<=C[-1]:
        return 2
    if ux>=mn-F('0.03'):
        return 3
    return 4
def AD(T,x):
    cc=CL(x)
    if T=='S':
        z=cc==1
        if h==1:
            z=z and U(x)>U(cm)
        return z
    if T=='I':
        z=cc==1 or cc==2
        if h==2:
            z=z and (PH(x)-x)*(cm-x)<=0
        return z
    z=cc==1 or cc==2 or cc==3
    if h==1:
        return False
    if h==2:
        z=z and U(x)>=U(cm)
    return z
def SC(x,e):
    z=RF(x)
    cs=(x-(-z))**2/2
    ps=U(x)-(-(z-z*x-b/2*z*z))
    out=[cs-(-e),ps-(-e),cs-(-ps)-(-e)]
    return out[h]
ps=[['0.806328','S','-0.008'],['0.100738','I','0.015'],['1.540594','S','-0.015'],['1.481586','Q','-0.015']]
st=[]
for i,pr in enumerate(ps,1):
    a=F(pr[0])
    T=pr[1]
    e=F(pr[2])
    adj=F(0)
    if prev=='S' and T=='Q':
        adj=u/4
    if prev=='Q' and T=='S':
        adj=-u/3
    x=cl(a-(-q)-(-adj),F(0),xm)
    st.append({'n':i,'a':a,'T':T,'e':e,'x':x,'c':CL(x),'ad':AD(T,x),'s':SC(x,e)})
rank=sorted(st,key=lambda z:(-z['s'],z['n']))
for z in st:
    print('S1',z['n'],z['T'],'x',z['x'],float(z['x']),'c',z['c'],'ad',z['ad'],'s',z['s'],float(z['s']))
print('RANK',[z['n'] for z in rank])
ads=[z for z in rank if z['ad']]
print('ADS',[z['n'] for z in ads])
def S2(z):
    off={'S':u,'I':-u/3,'Q':-u/2}[z['T']]
    x2=cl(z['x']-(-off),F(0),xm)
    sc=SC(x2,z['e'])
    if z['T']==prev:
        sc=sc-(-F('0.01'))
    return {'n':z['n'],'T':z['T'],'x2':x2,'c2':CL(x2),'ad':AD(z['T'],x2),'s':sc}
for z in ads[:2]:
    w=S2(z)
    print('S2',w['n'],w['T'],'x2',w['x2'],float(w['x2']),'c2',w['c2'],'ad',w['ad'],'s',w['s'],float(w['s']))
EOF