How can I find the set of distinct positive integers $\mathbb S=\{a, b, c, d, e, f, g, h, i\}$ such that:

1. $a+b$, $b+c$, $a+c$ are squares,
2. $d+e$, $e+f$, $d+f$ are squares,
3. $g+h$, $h+i$, $g+i$ are squares,
4. $a+b+c = d+e+f = g+h+i$ is square?

If there are several solutions then choose with minimal $a+b+c$.