how do I show that $S^1 \times S^1 \ldots \times S^1 $ is diffeomorphic to $\mathbb{T}^n$ as manifolds? Where $S^1 \times S^1 \ldots \times S^1 $ has the natural differential structure of a product manifold and $\mathbb{T}^n$ is obtained by the action of the group of integer translation of $\mathbb{R}^n$ in $\mathbb{R}^n$
ADDED(04/05/12):
I defined $f$ as in comments, proved that it is a bijection, and stuck here...