Help:=proc():print(`C(n),Rev1(S),Pref1(S,a)`):
print(`N(v),P(v)`):
end:


Rev1:=proc(S) local i,n: 
n:=nops(S):
[seq(S[n-i+1],i=1..n)]:
end:

#Pref1(S,a): Given a list of lists S, prefixes a to each of them
Pref1:=proc(S,a) local i:[ seq( [a,op(S[i])], i=1..nops(S))]:end:


C:=proc(n::nonnegint) local S,S1:
option remember:
if n=0 then
 return [[]]:
fi:

S:=C(n-1):
S1:=Rev1(S):
 [op(Pref1(S,0)),op(Pref1(S1,1))]:
end:

#N(v): next-in-line in C(n)
N:=proc(v) local n,v1,v1n: n:=nops(v):
if n=0 then
 RETURN(FAIL):
fi:

if n=1 then
if v[1]=0 then
  RETURN([1]):
else
  RETURN(FAIL):
fi:
fi:

v1:=[op(2..n,v)]:


if v[1]=0 then

 v1n:=N([op(2..n,v)]):
 
if v1n=FAIL then
   RETURN([1,op(v1)]):
 else
   RETURN([0,op(v1n)]):
 fi:

elif v[1]=1 then
 v1n:=P([op(2..n,v)]):
  if v1n=FAIL then
       RETURN(FAIL):
  else
   RETURN([1,op(v1n)]):
  fi:
else
  ERROR(`entries must be 0 or 1`):
fi:     
end:


#P(v): next-in-line in C(n)
P:=proc(v) local n,v1,v1p: n:=nops(v):
if n=0 then
 RETURN(FAIL):
fi:

if n=1 then
if v[1]=1 then
  RETURN([0]):
else
  RETURN(FAIL):
fi:
fi:

v1:=[op(2..n,v)]:


if v[1]=0 then

 v1p:=P([op(2..n,v)]):
 
if v1p=FAIL then
   RETURN(FAIL):
 else
   RETURN([0,op(v1p)]):
 fi:

elif v[1]=1 then
 v1p:=N([op(2..n,v)]):
  if v1p=FAIL then
       RETURN([0,op(v1)]):
  else
   RETURN([1,op(v1p)]):
  fi:
else
  ERROR(`entries must be 0 or 1`):
fi:     
end:


N1:=proc(v) local k,n:
n:=nops(v):
k:=convert(v,`+`):

if k mod 2 =0 then
  RETURN([op(1..n-1,v),1-v[n]]):
else

 if k=1 and v=[1,0$(n-1)] then
    RETURN(FAIL):
 fi:

end: