Fundamental group of degree 4 del Pezzo surface minus 16 (-1)-curves [Reference request]

Question

Let $S$ be a degree $4$ del Pezzo surface (over $\mathbb{C}$).

That is, $5$ points blow-up of $\mathbb{P}^2$, or $4$ points blow-up of $\mathbb{P}^1 \times \mathbb{P}^1$.


The classical fact is that $S$ has $16$ $(-1)$-curves.

My question is

What is the fundamental group of $S$ minus all $16$ $(-1)$-curves?

I appreciate any advice, answers, or references.