Gaia-2MASS diagram for our sample stars. The curved solid line delineates the theoretical limit between the O-rich (cyan symbols) and AGB C-stars (red symbols). Dashed lines separate the sub-groups of stars, as indicated in the figure. The circles correspond to $M_{K_s}$ magnitudes derived using phot-geometric DR3 distances from Bailer-Jones et al. (2021) and extinction from Lallement et al. (2022). For comparison, open triangles show the same but using distances and extinction values from Hunt & Reffert (2023). The uncertainty in $M_{K_s}$ is typically ±0.28 mag.