409439: GYM103561 D City View

Sadio has set up a grand night for Valentine's day. After dinner and dessert, he plans to take his significant other to the top of the tallest building in the city and use the lens he set up there to show his significant other the $$$n$$$ places around the city where they had memorable moments (date spots, favorite restaurants, etc).

Sadio goes to test the lens out before the big night and realizes that moving and refocusing the lens takes way too much time. To fix this, he decides to buy a new lens that captures enough of an angle in order to see all $$$n$$$ places at the same time. The cost of the lens increases linearly with the angle that it captures (so a lens that captures $$$90$$$ degrees would cost more than that which captures $$$89$$$ degrees). Note, when we say that the lens captures x degrees, it is equivalent to having two rays from the origin which make an angle of x degrees, and all the points on/within the two rays are seen.

The city can be represented as a grid where the tallest building (so where Sadio and his partner will be) is at $$$(0, 0)$$$ and each of the $$$n$$$ special points is located at integer coordinates $$$(x, y)$$$. Given that Sadio has already spent so much money planning tonight, he wants to spend as little as possible on the new lens. What is the minimum angle such that the lens with that angle can view all $$$n$$$ locations? The lens can view a location even if that location is on the very border of what the lens can see.

The first line contains a single integer $$$n$$$ (where $$$1 \leq n \leq 10^{5}$$$) which represents the number of special places.

The next $$$n$$$ lines each contain two space-separated integers $$$x_{i}$$$ and $$$y_i$$$ which represent the coordinates of the $$$i$$$th special place ($$$-1000 \leq x_i, y_i \leq 1000$$$).

It is guaranteed that no two special places are at the same point and there is no special place at $$$(0, 0)$$$.

A single decimal which equals the minimum angle, in degrees, such that all $$$n$$$ points are contained. The answer will be considered valid if the relative or absolute error doesn't exceed $$$10^{-6}$$$.

2
3 0
0 3

90.0000000000

3
-3 0
0 3
-3 -3

135.0000000000