Let the position vectors of the points A, B, C and D be $5 \hat{i}+5 \hat{j}+2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}$ and $\hat{-i}+5 \hat{j}+6 \hat{k}$ Let the set $S=\{\lambda \in R$ : The points $A, B, C$ and $D$ are coplanar $\}$. Then $\sum_{\lambda \in S}(\lambda+2)^2$ is equal to