Complex Numbers

For \(\mathrm{n} \in \mathbf{N}\), let \(\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}\) and \(\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}\). Then the number of elements in the set \(\left\{n \in \mathbf{N}: S_{n} \cap T_{n}=\phi\right\}\) is :