MLE of an exponential mean restricted to integers

Let $x_1=1.1$, $x_2=2.2$ and $x_3=3.3$ be the observed values of a random sample of size three from a distribution with the probability density function

$$f(x;\theta)=\begin{cases}\dfrac1\theta e^{-x/\theta}, & x>0,\ 0, & \text{otherwise,}\end{cases}$$

where $\theta\in\Theta=\{1,2,…\}$ is the unknown parameter. Then the maximum likelihood estimate of $\theta$ equals ____________