Solar 24V charge 12V inverter

I have a 12v inverter and 12v battery bank.

My charge controllers can double their capacity to charge a 24v bank vs 12v.

I am looking to figure out a way to arrange the 12v batteries to charge in 24v and run the 12v inverter.

Trying to keep it simple here...

#1 BAT + & #1 Bat - To INVERTER
#2 BAT + to #3 bat -
#2 Bat - and #3 bat + To charge controller
#2 Bat + to #1 bat + and #2 Bat - to #1 Bat -

I feel the 3rd battery will not be part of the battery bank, and he 2nd battery will not charge properly.

Any suggestions?

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Solar 24V charge 12V inverter