8939: Anticomplementary Triangle

链接：https://ac.nowcoder.com/acm/contest/57355/B
来源：牛客网
There are n points P1,P2,…,Pn in a plane forming a convex polygon. The coordinates of the $i$-th point Pi are (xi,yi). You need to find three pairwise distinct indices r,s,t∈{1,2,…,n}, such that there exists a triangle △ABC satisfying

• △ABC is the anticomplementary triangle of △PrPsPt.

• Pi is inside or on the edge of △ABC for all 1≤i≤n1.

△ABC is the anticomplementary triangle of △XYZ if X,Y,Z are the midpoints of edge BC,CA,AB respectively.

The first line contains an integer n (3≤n≤106), indicating the number of points.
The i-th of the next n lines contains two integers xi and yi (∣xi∣,∣yi∣≤10^9), indicating the coordinates of Pi. The vertices are guaranteed to form a convex polygon, and are given in counterclockwise order.

Output three integers r,s and $t$ indicating the selected indices. If there are multiple solutions, print any of them. You can output r,s,t in an arbitrary order.