Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $\mathrm{P}=\left[\mathrm{p}_{\mathrm{ij}}\right]$ be a $\mathrm{n} \times \mathrm{n}$ matrix with $\mathrm{p}_{\mathrm{ij}}=\omega^{\mathrm{i}+\mathrm{j}}$. Then $P^2 \neq 0$, when $n=$
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