Let \(\displaystyle S = \left\{ n \in \mathbb{N} \;\middle|\; \begin{pmatrix} 0 & i \\ 1 & 0 \end{pmatrix}^n \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \forall a, b, c, d \in \mathbb{R} \right\}\), where \( i=\sqrt{-1} \). Then the number of \( 2 \)-digit numbers in the set \( S \) is __________ .
