Given point $P_0$ in the plane of triangle $A_1A_2A_3$. Denote $A_s = A_{s-3}$, for $s > 3$. Construct points $P_1; P_2; \cdots$ sequentially such that point $P_{k+1}$ is $P_k$ rotated $120^\circ$ counter-clockwise around $A_{k+1}$. Prove that if $P_{1986} = P_0$ then triangle $A_1A_2A_3$ is isosceles.