Nagata's conjecture on Zariski chambers of the exceptional ray

Let $X$ be the blow-up of ${\mathbb P}^2$ at a set of $n$ general points, let $H$ be the hyperplane class, and let $\mathbb E=E_1+\cdots+E_n$ be the exceptional divisor. Nagata's conjecture. The ray $H-t\mathbb E$ for $t\geqslant 0$ crosses only one Zariski chamber before leaving $\overline{\operatorname{Eff}}(X)$. The source presents this as an equivalent formulation of Nagata's conjecture; no resolution status is supplied.