Singularities on the base of a Fano type fibration

Let $f\text{\hspace{0.17em}⁣}:X\to Z$ be a Mori fibre space. McKernan conjectured that the singularities of $Z$ are bounded in terms of the singularities of $X$. Shokurov generalised this to pairs: let $(X,B)$ be a klt pair and $f\text{\hspace{0.17em}⁣}:X\to Z$ a contraction such that $K_X+B{\sim }_{\mathbb{R}}0\mathrm{/}Z$ and that the general fibres of $f$ are Fano type varieties; adjunction for fibre spaces produces a discriminant divisor $B_Z$ and a moduli divisor $M_Z$ on $Z$. it is then conjectured that the singularities of $(Z,B_Z+M_Z)$ are bounded in terms of the singularities of $(X,B)$. We prove Shokurov conjecture when $(F,\text{Supp}{B}_F)$ belongs to a bounded family where $F$ is a general fibre of $f$ and $K_F+B_F=(K_X+B){\mathrm{\mid }}_F$.