Chemical modeling using 3D-DPR to identify the best range of the CR ionization parameter ζ_CR/n_H (x-axis) based on the observed column density ratios. The column densities of HCN (blue), HCO⁺ (orange), and HNC (green) are normalized with CS. The y-axis shows the ratio of the modeled column density ratio to the observed one. Unity marks agreement between the models and observations. The upper panel shows the results for APM 08279+5255, and the lower panel shows those for NCv1.143. The insets are zoom-in regions of the gray rectangular area in each panel. The thickness of each line represents the uncertainty (light color is for 50% uncertainty, and dark color is for 10% uncertainty).