Find all number sets $(a, b, c, d)$ s.t. $1 < a \le b \le c \le d, a,b,c,d \in\mathbb{N}$, and $a^2 + b + c + d, a + b^2 + c + d, a + b + c^2 + d$ and $a + b + c + d^2$ are all square numbers. Sum the value of $d$ across all solution $set(s)$.