

Help with making a rechargeable DC fan
Because the frequent power blackouts in my country, I have at hand a desk fan with a 12V 0.5A fan, so I purchased a 3S 40A BMS and 6x 18650 batteries to be charged by the BMS. The battery wiring is exactly like the 1st picture. I also got a 12.6V Li-Ion charger (2nd picture).
I'm aware that I need to wire the DC adapter's positive lead to the BMS' positive pad and the same for the negative lead. But what about the actual fan (with its own switch)???
Do I wire it parallel to the charger and BMS???? Do I need diodes???
The freaking AI suggested 2 diodes, one from the DC jack positive terminal to the diode's anode, and the other diode from the BMS' positive terminal joined at the cathode and then that joint part goes to the switch. But I fear that with that, instead of 12.6V, the BMS will receive less voltage because of the Diodes.
Can you help me out the correct diagram to wire the BMS to a DC fan???
My goal is to keep the fan on on battery, but also on wall power. If possible, to be able to run the fan and charge the batteries at the same time.