python3 -c 'import itertools
S=0
for t in itertools.product(range(2),repeat=10):
 w=list(t)
 z=10-sum(w)
 if z%4==0:continue
 C=sum(1 for i in range(9) if w[i]!=w[i+1])
 N=sum(1 for i in range(9) if w[i]==0 and w[i+1]==0)
 M=1
 r=1
 for i in range(1,10):
  if w[i]==w[i-1]:
   r+=1
  else:
   if r>M:M=r
   r=1
 if r>M:M=r
 O=sum(w[i] for i in range(0,10,2))%2
 S+=(-1)**(C+O+1)*(16*C+7*M+13*N+2**(O+2)+5)
print(S%1091)'