Find all number sets (a, b, c, d) s.t. 1<a \leq b \leq c \leq 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).
Find all number sets (a, b, c, d) s.t. 1<a \leq b \leq c \leq 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).