$11\times13\times7=1001$  $1+3+7+0=11$ 
In the calculation shown below, different letters represent different digits.  $AA\times AB\times C=ADDA$  What is the sum of $A+B+C+D$? 
Options:
$$9$$ 
$$11$$ 
$$13$$ 
$$16$$ 
$$18$$ 