#John Kim
#Use whatever you like

#read "C:/Users/John Y. Kim/Documents/Maple/hw22.txt":


split:=proc(L,R)
local n,m:
if nops(L)=0 or nops(R)=0 then
 RETURN(false):
fi:
 
n:=op(nops(L),L):
m:=op(1,R):
 
if n=m then
 RETURN(false):
fi:
 
if n>=4 and m<=3 then
RETURN(true):
fi:
 
if n=2 then
 if m=1 and nops(R)>2 and op(2,R)<>1 and op(3,R)<>op(2,R) then 
   RETURN(true):
 fi:
 if m=1 and nops(R)=2 and op(2,R)<>1 then 
   RETURN(true):
 fi:
 
 if m=1 and nops(R)>=3 and op(2,R)=1 and op(3,R)=1 then 
   RETURN(true):
 fi:
 
 if m=3 and nops(R)>=2 and op(2,R)<>3
and not(nops(R)>=4 and op(2,R)=op(3,R) and op(3,R)=op(4,R))
 then
        RETURN(true):
 fi:
 
 if m=3 and nops(R)=1 
 then
        RETURN(true):
 fi:
 
 if m>=4 then
  RETURN(true):
 fi:
fi:
 
if n<>2 then
  if nops(R)>=5 and op(1,R)=2 and op(2,R)=2 and op(3,R)=1 and op(4,R)<>1
     and op(5,R)<>op(4,R)  then
      RETURN(true):
  fi:
 
  if nops(R)=4 and op(1,R)=2 and op(2,R)=2 and op(3,R)=1 and op(4,R)<>1 then
      RETURN(true):
  fi:
 
 if nops(R)>=5 and op(1,R)=2 and op(2,R)=2 and op(3,R)=1 and op(4,R)=1
              and op(5,R)=1 then
    RETURN(true):
 fi:
 
 if nops(true)>=4 and op(1,R)=2 and op(2,R)=2 and op(3,R)=3 and op(4,R)<>op(3,R)
              and not(nops(R)>=6 and op(4,R)=op(5,R) and op(5,R)=op(6,R))
                 then
    RETURN(true):
 fi:
 
 if nops(R)=2 and op(1,R)=2 and op(2,R)=2 then
  RETURN(true):
 fi:
 
 if nops(R)=3 and op(1,R)=2 and op(2,R)=2 and op(3,R)>=4 then
  RETURN(true):
 fi:
 
 if nops(R)>=3 and op(1,R)=2 and op(2,R)=2 and op(3,R)>=4 and
                     op(4,R)<>op(3,R)    then
                   
  RETURN(true):
 fi:
fi:
false:
end:
 




#IsAtom(L): inputs a list in {1,2,3}*, L, and outputs true 
#iff L is an atom.

IsAtom:=proc(L) local i:

if L=[] then
 false:
elif L=[3] then
 true:
elif L=[1] or L=[2] then
 false:
else
 for i from 1 to nops(L)-1 do
  if split(L[1..i],L[i+1..nops(L)]) then
   RETURN(false):
  fi:
 od:

 RETURN(true):
fi:

end:


#SplitUp(L): inputs a list in {1,2,3}*, L, and outputs it as a 
#list of lists
#[L1,L2,L3, ...]
#where L=[op(L1),op(L2), op(L3), ...]
#and L1,L2,L3,... are atoms. 

SplitUp:=proc(L) local i,L1,Lrest:
option remember:

if IsAtom(L) then
 RETURN([L]):
fi:

for i from 1 to nops(L)-1 do
 L1:=L[1..i]:
 Lrest:=L[i+1..nops(L)]:
 
 if split(L1,Lrest) then
  RETURN([L1,op(SplitUp(Lrest))]):
 fi:
od:

end: