Given a positive integer $n(n \geqslant 2)$. Find the largest positive real number $C$, such that for any $x_{1}, x_{2}, \cdots, x_{n}$, we have
$$
\sum_{i=1}^{n} x_{i}^{2} \geqslant \frac{1}{n+1}\left(\sum_{i=1}^{n} x_{i}\right)^{2}+C\left(\sum_{i=1}^{n} i x_{i}\right)^{2} .
$$