ACC for lengths of extremal rays of log canonical Fano varieties with Picard number one

Let $X$ be an $n$-dimensional $\mathbb Q$-factorial log canonical Fano variety with Picard number one, and define

$$l(X):=\min_C(-K_X\cdot C),$$

where $C$ is an integral curve on $X$. Set

$$\mathcal L_n:=\left\{l(X)\;\ X\text{ is an }n\text{-dimensional }\mathbb Q\text{-factorial log canonical Fano variety with Picard number one}\right\}.$$

ACC for lengths of extremal rays. For every $n$, the set $\mathcal L_n$ satisfies the ascending chain condition: if $X_k$ is an $n$-dimensional $\mathbb Q$-factorial log canonical Fano variety with Picard number one for every $k$ and

$$l(X_1)\leq l(X_2)\leq\cdots\leq l(X_k)\leq\cdots,$$

then there is a positive integer $l$ such that $l(X_m)=l(X_l)$ for every $m\geq l$.

The paper proves this assertion for $n$-dimensional $\mathbb Q$-factorial toric Fano varieties with Picard number one, while the stated general ACC remains open.