How many different solutions has this equation:

$\displaystyle \overline{abc}+\overline{def}+\overline{ghi}=963$

Here $\displaystyle \overline{abc}, \overline{def}, \overline{ghi}$ are three-digit numbers

$\displaystyle a,b,c,d,e,f,g,h,i $- different digits; $\displaystyle a,d,g\neq 0$

I could begin with:

$\displaystyle (a+d+g)\cdot100+(b+e+h)\cdot10+(c+f+i)=963$

Now, $\displaystyle c+f+i$ must be 3, 13 or 23...

Not know how to connect with other.

Could you help to me. Thank you!!!