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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

hide comments
2016-01-11 17:35:28 Mitch Schwartz
@Dominique Thanks, I didn't see your comment until now.
2015-09-04 11:22:19 Dominique VAILLANT
@Mitch: POLYGONA, INTER, CONTFRAC, TETRAHE1,... what a great firework in Ruby!
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