Bias of the gamma rate MLE

Let $X_1, X_2, \dots, X_7$ be a random sample from a population having the probability density function $f(x) = \frac{1}{2} \lambda^{3} x^{2} e^{-\lambda x}, \; x > 0$, where $\lambda > 0$ is an unknown parameter. Let $\hat{\lambda}$ be the maximum likelihood estimator of $\lambda$, and $E(\hat{\lambda} - \lambda) = \alpha \lambda$ be the corresponding bias, where $\alpha$ is a real constant. Then the value of $\frac{1}{\alpha}$ equals __________ (answer in integer).