AMC 8 2017 Problem 21

Suppose $a$, $b$, and $c$ are nonzero real numbers, and $a+b+c=0$. What are the possible value(s) for $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}$? $\text{(A) }0 \text{(B) }1\text{ and }-1 \text{(C) }2\text{ and }-2 \text{(D) }0,2,\text{ and }-2 \text{(E) }0,1,\text{ and }-1$