help with 3 pairs of 3 way switches in series

Hello,
I'm finishing my basement. I'd like to know if this is possible. Three lights controlled by three pairs of 3-way switches. 1st light in gym, 2nd light in office, 3rd light in hallway. I'd like to be able to control each light in each area at the entry and exit points.

From the electrical panel 14/2 cable to first single gang 3-way switch that will be at front of gym. 14/3 from first single gang to double gang that will be at end of gym and front of office area. This double gang has two 3-way switches, one for gym, one for office. Then a second double gang with two 3-way switches, one for office and one for hallway. Then finally a single gang with a 3-way switch at end of hallway.

For extra points! :thumbup: Actually. I'd like to have two lights in the gym area.

I'd like someone to explain if and how this can be done.

Thanks in advance!

Steve