f=\
lambda b:next(C(b),0)!=0
R,T,U=range,sorted,lambda x:''.join(map(str,x)).lstrip('0')
Z=zip
def C(b):
 q,S=[([],0)],[]
 while q:
  r,c=q.pop(0);L=len(b)
  if all(a==sum(j)for a,j in Z(b,Z(*r)))*r:yield r
  if c==L:1
  elif b[c]:
   for i in{*R(1,b[c]+1)}-{j for k in r for j in k}:
    for g in R(1,L+1):
     k=[0]*L;k[c]=i;I=1
     while I*g+c<L or c>=I*g:
      if c>=I*g:k[c-I*g]=i
      if I*g+c<L:k[I*g+c]=i
      I+=1
     if all(a>=sum(j)for a,j in Z(b,Z(*r+[k])))>any(all(j==K for j,K in Z(U(i),U(k)))for i in r)==(T(r+[k])in S):q+=(K:=r+[k],c+1),;S+=T(K),;q+=(b[c]>sum(j[c]for j in K))*[(K,c)]
  else:q+=(r,c+1),
 
print(f([0,1,1,0,1,1,0,1,1,0]))
print(f([0,1,1]))
print(f([1,1,2]))
print(f([2,9,2,6,1]))
#print(f([9,2,8,7,3,6,1,1]))
#print(f([9,10,7,3,8,8,2,2])) Times out
print('-'*20)
print(f([9]))
print(f([9,9]))
print(f([9,9,9]))
print(f([9,9,9,9]))
print(f([0,3,3]))
print(f([3,1,1]))
print(f([0,3,3,0,3,3,0,3,3,0]))
print(f([1,2,3,4,5,6,7,8]))
#print(f([9,9,9,9,9,9,9,9,1]))
#print(f([5,7,5,3,9,4,5,7]))

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