Find all possible solutions to the system of equations:

(i) n(p) + n(q) = p;
(ii) p+q+ n(r) = r;
(iii) n(p) + n(q) + n(r) = q - 4;

where, each of p, q and r are positive integers and n(p), n(q) and n(r) respectively denote the number of digits of the integers p, q and r.