f=open("out_27_18_7.txt","w")
def hamiltonian(h,l,m,k=[]):
       k=k+[l]
       if l==m:
              return [k]
       if not h.has_key(l):
              return []
       n=[]
       for i in h[l]:
              if i not in k:
                     w=hamiltonian(h,i,m,k)
                     for a in w:
                                   if len(a)==len(h):
                                          n.append(a)
                     
       return n

h={'U': ['V','W','Z'],'V': ['U','X','Y'],'W': ['U','X','Z'],'X': ['W','V','Y'],'Y': ['V','X'],'Z': ['W','U']}
r=hamiltonian(h,'U','Z')
z=str(r)
f.write(z+"\n")
f.close()