Rectangles#4471
A polygon is given in the plane. Find the rectangle of minimal area that can contain (enclose) the given polygon entirely.
For example, for the following polygon:
the corresponding rectangle is:
The input consists of the integer (3 \leq N \leq 3000) on the first line — the number of vertices of the polygon. Each of the following lines contains two real numbers X_i and Y_i — the coordinates of the -th vertex of the polygon listed in clockwise order.
All coordinates in the input and output files are given as real numbers in standard input/output format. The recommended data type for coordinates is Real in Pascal and float in C/C++.
The output should consist of lines. The first line must contain the real number — the area of the minimal rectangle. The following lines must each contain two real numbers X_i Y_i — the coordinates of the rectangle's vertices, in order of traversal (any direction).
The area and the rectangle's coordinates must be computed with a precision of at least 10^{-5}.
Example 1