67. As shown in the figure, in the Cartesian coordinate system $x O y$, the vertices of the isosceles trapezoid $A B C D$ have coordinates $A(1, 1)$, $B(2, -1)$, $C(-2, -1)$, $D(-1, 1)$. A point $P(0, 2)$ on the $y$-axis is rotated $180^{\circ}$ about point $A$ to get point $P_{1}$, point $P_{1}$ is rotated $180^{\circ}$ about point $B$ to get point $P_{2}$, point $P_{2}$ is rotated $180^{\circ}$ about point $C$ to get point $P_{3}$, and point $P_{3}$ is rotated $180^{\circ}$ about point $D$ to get point $P_{4}, \cdots \cdots$, repeating the operation to sequentially obtain points $P_{1}$, $P_{2}, \cdots \cdots$. What are the coordinates of point $P_{2021}$? $\qquad$
Answer: $(-2018,0)$