Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin $p_0=(0,0)$ facing to the north and walks one unit, arriving at $p_1=(0,1)$. For $n=1,2,3,\dots$, right after arriving at the point $p_n$, if Aaron can turn $90^{\circ }$ right and walk one unit to an unvisited point $p_{n+1}$, he does that. Otherwise, he walks one unit straight ahead to reach $p_{n+1}$. Thus the sequence of points continues $p_2=(1,1)$, $p_3=(1,0)$, $p_4=(1,-1)$, $p_5=(0,-1)$, and so on in a clockwise spiral pattern. What is $p_{2020}$?