Triangles (Bronze)

Triangles (Bronze)

Farmer John would like to create a triangular pasture for his cows. There are n fence posts at distinct points (x1, y1) . . .(xn, yn) on the 2D map of his farm. He can choose three of them to form the vertices of the triangular pasture as long as one of the sides of the triangle is parallel to the x-axis and another side is parallel to the y-axis.

What is the maximum area of a pasture that Farmer John can form? It is guaranteed that at least one valid triangular pasture exists.


The first line contains the integer n (3n100). Each of the next n lines contains two integers xi and yi, each in the range −104.... 104 inclusive, describing the location of a fence post.


As the area itself is not necessarily an integer, output two times the maximum area of a valid triangle formed by the fence posts.

Time limit 1 second
Memory limit 128 MiB
Input example #1
0 0
0 1
1 0
1 2
Output example #1
Source 2020 USACO February Bronze