Flat Owners don't repair their flats causing damage to other flats and refuse to repair.

Hi, I live on the ground floor of a poorly maintained housing society. The flats on the upper floors haven't done even basic maintenance of their sink, bathroom and toilet area ever since the building was constructed. Sink water and bathroom water is now constantly leaking from the 2nd and 3rd floor flats right onto my the entry door and walls of my flat causing severe damage. Moreover, that entire wall of the building is rotting in the process. When the matter was brought to the notice of the flat owners, one owner point blank refused to spend a single penny on repairs. The other flat owner doesn't stay in the flat and has rented it out to a tenant. When contacted via phone call, they too refused to carry out repairs. Both these shameless flat owners are asking me to carry out the repairs for their flats if I have problem with leakages! When I approached the housing society management, they brushed off this issue stating that it is a 'bilateral' problem between flat owners and refused to intervene. I asked the plumbing repairman and he stated that the repairs will cost quite a tidy sum. I want to know that if I spend money on repairing the plumbing work of these flats, is there any legal recourse by which I can force the society to recover money from them? Or should I as the suffering flat owner directly send them a legal notice? Or can I inform the housing society about the repair work I carried out and then inform them that I won't be paying maintenance. Please provide a solution to my dilemma.