I want to compute the following integral

$\displaystyle \oint_{|z|=1}\frac{\exp(\frac{1}{z})}{z^2-1}\,dz$

The integrand has essential singularity at the origin, and 2-poles at $\displaystyle \pm 1$,which lie on the curve $\displaystyle |z|=1$ so i can't apply residue formula. How can i proceed?