For n ∈ N, let S_n ={z ∈ C:|z-3+2 i|=n/4} and T_n ={z ∈ C:|z-2+3 i|=1/n}. Then the number of elements in the set { n ∈ N: S_n ∩ T_n =φ} is:

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