Group theory/Exact sequences/Product formula/Exercise

Let

G_{0} \to G_{1} \to \dots \to G_{n - 1} \to G_{n}

be an exact sequence of groups, where all groups are finite, and where $G_{0} = G_{n}$ are the trivial group. Show that

\prod_{i = 0}^{n} {# (G_{i})}^{(- 1)^{i}} = 1

holds.