Let $S$ denote the set of all real values of $\lambda$ such that the system of equations $$ \begin{aligned} & \lambda x+y+z=1 \ & x+\lambda y+z=1 \ & x+y+\lambda z=1 \end{aligned} $$ is inconsistent, then $\sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to [JEE Main 2023, 1 Feb (Shift 1)]

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