Find the THREE Numbers

A triplet of integers $(A,B,C)$ is considered to be special if it satisfies the following properties for a given integer $N$ : $A mod B=C$ $B mod C=0$ $1 \leq A,B,C \leq N$ Example: There are three special triplets for $N=3$. (1,3,1) is a special triplet, since $ (1 mod 3)=1$ and $(3 mod 1)=0$. (1,2,1) is a special triplet, since $(1 mod 2)=1$ and $(2 mod 1)=0$. (3,2,1) is a special triplet