Mean of a variable whose conditional law is uniform on zero to y

Let $Y\sim U(0,1)$. The conditional probability density function of $X$ given $Y$ is

$$f_{X|Y}(x|y)=\begin{cases}\frac1y, & 0<x<y<1,\ 0, & \text{otherwise.}\end{cases}$$

Then $E(X)=$ ___________.