GATE DA 2026 Q65: Maximum of xᵀAx on the unit sphere for the centering matrix

Let $A = \left(I_n - \dfrac{1}{n}\mathbf{1}\mathbf{1}^T\right)$ be a matrix, where $\mathbf{1} = (1, 1, 1, \ldots, 1)^T \in \mathbb{R}^n$ and $I_n$ is the identity matrix of order $n$.

The value of $\max_{S} x^T A x$, where $S = \{x \in \mathbb{R}^n \mid x^T x = 1\}$, is __________. (Answer in integer)