Pipe route question

In the attached drawing, I show a proposed pipe route for a 2" dwv from a bathroom sink to the main stack in a 2nd floor bathroom. I would like to know if the route is permissable and of not, can someone give me instructions on a better route.

I can not go straight and "put-in" a new stack due to existing heating ducts.

Also I would like to thank everyone on this forum. I have learned alot just from reading the questions and answers.

I accidently posted this in remodel forum

That part is okay if you do it correctly. However, I would like more info on your "wet vent" at the sink. From your drawing, it does NOT appear to be a wet vent, or even a correct vent. If this all that is on that system, you do not need the "Through the roof" section where it goes down to the basement.