Maximum eigenvalue of the centering projection matrix

Let $A = (I_n - \frac{1}{n}\mathbf{1}\mathbf{1}^T)$ be a matrix, where $\mathbf{1} = (1,1,1, … ,1)^T \in \mathbb{R}^n$ and $I_n$ is the identity matrix of order $n$. The value of $\max_{S} x^TAx$ , where $S = \{x \in \mathbb{R}^n \mid x^Tx = 1\}$, is __________ . (Answer in integer)