Consider the rotation $$T$$ of space with $$T(0,0,0)=(0,0,0)$$, $$T(6,6,3)=(4,-1,8)$$ and $$T(-6,3,6)=(4,8,-1)$$. If $$T(3,9,12)=(a,b,c)$$, find $$a+b+c$$.