Categorical genus for log del Pezzo surfaces with cyclic quotient singularities

For the canonical stack $\mathcal{X}$ of a log del Pezzo surface with cyclic quotient singularities, we compute its categorical genus as \[ g_{\mathrm{cat}}(\mathcal{X})= 1+\frac{1}{2}\sum_j w_j(\ell_j-1), \] where $w_j=\gcd(n_j,q_j+1)$ and $\ell_j=n_j/w_j$ are the local widths and Gorenstein indice