Gaia-2MASS diagram for our main star sample. The curved line delineates the theoretical limit between O-rich (left of the line) and C-rich AGB stars (right of the line). Dashed lines separate sub-groups of stars as indicated in the figure. The colour code for the different AGB types is shown in the bottom right corner. Open blue circles show N-type stars for clarity. Several SC-type stars (green circles) and J-type stars (red circles) are placed in the C-rich zone, but cannot be distinguished in the figure because of crowding. The uncertainty in M_Ks typically is ±0.23 mag.