I'm a Fan

Sangsu is a devoted fan of Jinpyo. As a token of his fandom, he gives Jinpyo a fan that he built himself. While playing with it, Jinpyo discovers that once the fan is turned past a certain angle, the path traced by its blades becomes a circle.

Suppose the fan blades lie on a coordinate plane whose origin is the fan's center of rotation. The blades can then be represented as a simple polygon with N vertices that contains the origin. For safety, the blades were designed to satisfy the following condition.

For any point P inside the fan blades, every point on the line segment connecting the origin O to P is also inside the blades.

Find the minimum rotation angle at which the path traced by the blades becomes a circle. The fan turns counterclockwise.

The first line gives the number of vertices N of the fan blades (3 ≤ N ≤ 300,000).

The next N lines give the coordinates of the vertices in counterclockwise order. Each coordinate consists of two integers, an x coordinate and a y coordinate, and the absolute value of each coordinate is at most 10^6.

The polygon contains the origin, and no two sides intersect except for adjacent sides. No three consecutive points of the polygon lie on a single line.

Print the minimum angle θ, in degrees, such that turning the fan counterclockwise by θ makes the path traced by the blades a circle. An absolute or relative error of at most 10^-6 is accepted.

The fan from the first example is shown below.

When it is turned 45° counterclockwise, the traced path is as follows. The first and last shapes are shaded dark.

Once it has turned 90°, the traced path becomes a circle of radius 2√2. The answer is therefore 90.