Pairs upstairs

Calculate

$\displaystyle\ln\sum\limits_{\gamma_1\in\{-1,1\}}\ldots\sum\limits_{\gamma_{2014}\in\{-1,1\}}e^{\gamma_1\gamma_2}\ldots e^{\gamma_{2013}\gamma_{2014}}$

This kind of summation has applications in the statistical mechanics of magnets and simple models of neural networks.