Empty Convex Polygons

Time Limit: 16000/8000 MS (Java/Others)

Memory Limit: 262144/262144 K (Java/Others)

Description

Given a set of distinct points S on a plane, we define a convex hole to be a convex polygon having any of thegiven points as vertices and not containing any of the given points in its interior. In addition to the vertices, other given points may lie on the perimeter of the polygon. We want to find a convex hole as above forming the convexpolygon with the largest area.

Input

This problem has several test cases.
The first line of input contains an integer t (1 ≤ t ≤ 100) indicating the total number of cases. For each test case,the first line contains the integer n (3 ≤ n ≤ 50). Each of the following n lines describes a point with two integers x and y where -1000 ≤ x, y ≤ 1000.
We guarantee that there exists at least one non-degenerated convex polygon.

Output

For each test case, output the largest area of empty convex polygon, with the precision of 1 digit.
Remark: The corollary of Pick’s theorem about the polygon with integer coordinates in that says the area of it iseither ends to .0 or .5.

Sample Input

4 3 0 0 1 0 0 1 5 0 0 1 0 2 0 0 1 1 1 5 0 0 3 0 4 1 3 5 -1 3 6 3 1 1 0 2 0 3 0 4 0 5 0

Sample Output

0.5 1.5 17.0 2.0

Hint

jiangzijing2015

Source

2017ACM/ICPC亚洲区沈阳站-重现赛(感谢东北大学)

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