$n = 5$, and $m_ i, a_{ij}, w_ i, g_ i$ given by
\[ \left( \begin{matrix} m \\ 2m \\ 3m \\ 2m \\ m \end{matrix} \right), \quad \left( \begin{matrix} -2w & w & 0 & 0 & 0 \\ w & -2w & w & 0 & 0 \\ 0 & w & -2w & 2w & 0 \\ 0 & 0 & 2w & -4w & 2w \\ 0 & 0 & 0 & 2w & -4w \\ \end{matrix} \right), \quad \left( \begin{matrix} w \\ w \\ w \\ 2w \\ 2w \end{matrix} \right), \quad \left( \begin{matrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix} \right) \]with $w$ and $m$ arbitrary,
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