Convex hull
You are given a set of points on a plane.
Your task is to determine their convex hull.
Input
The first line of the input contains an integer n — the number of points (3 ≤ n ≤ 200,000). Each of the following n lines provides the coordinates of a point, with the i-th line containing two integers representing the i-th point's coordinates. These coordinates do not exceed 10^9 in absolute value. It is guaranteed that not all points are collinear. Points may overlap.
Output
On the first line of the output, print the number of vertices that make up the convex hull. On the second line, list the indices of these vertices in counterclockwise order, separated by spaces. Ensure that no two edges of the convex hull are collinear.
On the third line, print the perimeter of the convex hull, and on the fourth line, print its area.
The perimeter should be printed with an absolute or relative error not exceeding 10^{-9}. The area should be printed with absolute precision.