Let \(D=\{x^{(1)},\ldots,x^{(n)}\}\) be a dataset of \(n\) observations where…

Let $D=\{x^{(1)},\ldots,x^{(n)}\}$ be a dataset of $n$ observations where each $x^{(i)}\in\mathbb{R}^{100}$. It is given that $\sum_{i=1}^{n}x^{(i)}=0$. The covariance matrix computed from $D$ has eigenvalues $\lambda_i=100^{2-i}$, $1\le i\le 100$. Let $u\in\mathbb{R}^{100}$ be the direction of maximum variance with $u^\top u=1$.

The value of $\frac{1}{n}\sum_{i=1}^{n}(u^\top x^{(i)})^2=$

(Answer in integer)