Let $A = \{ 1,2,3,\ldots\ldots\ldots\ldots,100\}$, Let $R$ be a relation on $A$ defined by $(x,y) \subset R$ if and only if $2x = 3y$. Let $R_{1}$ be a symmetric relation on $A$ such that $R \subset R_{1}$ and the number of elements in $R_{1}$ is $n$. Then, the minimum value of $n$ is $\$ .