Polygon#4783
The Ministry of Defense of Flatland is tasked with modernizing its weaponry, which includes constructing a new testing range. This range is designed as a convex polygon. To facilitate the observation of military tests by various officials, an observation center needs to be built nearby. After thorough analysis, it was determined that the key factor for the location of the observation center is its degree relative to the polygon.
The degree of a point relative to the polygon is determined as follows: Consider all rays that start from point and intersect the polygon. For each ray, calculate the minimum and maximum distances from point to any point on the polygon, denoted as d_{min} and d_{max}, respectively. The degree of the point relative to the polygon is defined as the minimum value of d_{min} \times d_{max} across all such rays.
The military needs assistance in calculating the degree of the observation center relative to the polygon, and they have enlisted your help.
Assume the observation center is located at point . The input provides a description of the polygon.
The first line contains the integer — the number of vertices of the polygon (3 \leq n \leq 100). The following lines each contain two real numbers, representing the coordinates of the polygon's vertices in counterclockwise order. The coordinates do not exceed in absolute value. It is guaranteed that the observation center is outside the polygon, the polygon is a convex, non-degenerate polygon, and no three consecutive vertices are collinear. Additionally, no side of the polygon lies on a ray originating from the origin.
Output a single number — the degree of the observation center relative to the polygon. The result must be accurate to within 10^{-4}.
Example 1