Expectation of a two-point Poisson map

Let $X$ be a random variable having the Poisson distribution with mean $1$. Let $g:\mathbb{N}\cup\{0\}\to\mathbb{R}$ be defined by $$g(x)=\begin{cases}1,&\text{if }x\in\{0,2\},\ 0,&\text{if }x\notin\{0,2\}.\end{cases}$$ Then $E(g(X))$ is equal to