Method of moments for a Gamma shape

Let $x_1, x_2, \dots, x_n$ ($n \ge 2$) be the observed values of a random sample from the following probability density function $f(x) = \begin{cases} \frac{\lambda^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\lambda x}, & x > 0 \ 0, & \text{otherwise} \end{cases}$, where $\alpha \in (0, \infty)$ and $\lambda \in (0, \infty)$ are unknown parameters. If $\frac{x_1 + x_2 + \cdots + x_n}{n} = 2$ and $\frac{x_1^2 + x_2^2 + \cdots + x_n^2}{n} = 5$, then the method of moments estimate of $\alpha$ equals ________ (answer in integer).