From Me to You

Hina

There are $N$ statues in this area. If we regard the area as a two-dimensional plane, I am at $(0, 0)$, and the $i$-th statue is at $(x_i, y_i)$. We can treat each statue as a point. $(1 \leq i \leq N)$

Each time I use my machine gun, I can remove all statues in a sector centered at my position, with central angle $\theta$ and infinite radius. There are still statues to destroy in other areas, so I want to quickly remove every statue here using my machine gun only $2$ times. A larger $\theta$ takes more effort, so let us find the minimum $\theta$ that allows me to remove all the statues.

No point is at the origin $(0, 0)$, and no two points have the same coordinates.

Time limit

2000 ms

Memory limit

1024 MB

Checker

CUSTOM