HMMT 2016 G7

Let $S=\{(x, y) \mid x, y \in \mathbb{Z}, 0 \leq x, y, \leq 2016\}$. Given points $A=\left(x_{1}, y_{1}\right), B=\left(x_{2}, y_{2}\right)$ in $S$, define

$$d_{2017}(A, B)=\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2} (\bmod 2017)$$

The points $A=(5,5), B=(2,6), C=(7,11)$ all lie in $S$. There is also a point $O \in S$ that satisfies

$$d_{2017}(O, A)=d_{2017}(O, B)=d_{2017}(O, C)$$

Find $d_{2017}(O, A)$.