Let $g[n]=\left\{ \begin{array}{rcl} 1 & n=0 \\0 &n=\pm 1,\pm 2,\pm 3,\dots \end{array}\right. $ and $h[n]=\left\{ \begin{array}{rcl} 1 & n=0,3,6,9\dots \\0 & otherwise \end{array}\right. $
Consider $y[n]=h[n]\otimes g[n]$, where $\otimes$ denotes the convolution operator. The value of $y[2]$ is ___________