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

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

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