Let $X_1,...,X_n$ be points on $\mathbb S^1.$

We then define the expectation value $E(X)=\frac{1}{n}\sum_{i=1}^n X_i.$

Let $\frac{dS(X_1)}{2\pi}$ be the normalized surface measure of $\mathbb S^1,$ i.e. $X_i$ are uniformly distributed random variables on the circle.

I am curious to know:

How does

$$\int_{(\mathbb S^1)^n } \frac{1}{\vert E(X) \vert}\frac{dS(X_1)}{2\pi}...\frac{dS(X_n)}{2\pi}$$ scale with $n$?