JEE Math Practice Question

Let $$S$$ denote the set of all real values of $$\lambda$$ such that the system of equations $$\lambda x+y+z=1$$ $$x+\lambda y+z=1$$ $$x+y+\lambda z=1$$ is inconsistent, then $$\sum\limits_{\lambda \in S}\left(|\lambda|^{2}+|\lambda|\right)$$ is equal to

1. A.12
2. B.2
3. C.4
4. D.6