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

a+b,b+c,a+care squares,d+e,e+f,d+fare squares,g+h,h+i,g+iare squares,a+b+c=d+e+f=g+h+iis square?

If there are several solutions then choose with minimala+b+c.