KURSCHAK 1988 Problem 2

Set $T\subset\{1,2,\dots,n\}^3$ has the property that for any two triplets $(a,b,c)$ and $(x,y,z)$ in $T$ , we have $a<b<c$ , and also, we know that at most one of the equalities $a=x$ , $b=y$ , $c=z$ holds. Maximize $|T|$ .