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We are given the vectors $\overrightarrow{a}=(1;-2;-2)$, $\overrightarrow{b}=(0;1;3)$ and $\overrightarrow{c}=(1;-1;0)$. Find the mixed product $(\overrightarrow{a}\times \overrightarrow{b})\cdot \overrightarrow{c}$.