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POLYGONA - Area of an Irregular Polygon

This challenge is to calculate the area of an irregular convex polygon. For each test there will be an arbitrarily ordered list of x,y coordinates (integer, -1000 <= x,y <= 1000) for each point in the polygon. For each test there will be N points, where N <= 500.

Input

The first line will contain a single value T for the number of tests, T <= 100.

Each test will begin with a single value N for the number of points in that test, N <= 500. The following N lines will contain the x,y coordinates of the polygon's corners, where x and y are integers in the range -1000 to 1000.

Output

For each test case the output should be the area to one decimal place.

Example

Input:
3
3
0 0
100 0
200 100
4
-60 50
40 -30
60 50
-40 -30
5
0 -30
50 -90
200 0
0 -60
400 -60

Output:
5000.0
8000.0
21000.0

 Added by: Jander Date: 2012-04-22 Time limit: 5s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 SCM qobi