There is a convex polygon of vertices and you want to divide it into two convex polygons and such that their areas are equal (half of ) and the sum of perimeters of and is minimum possible.
The first line of the input is an integer which denotes the number of test cases.
For each test case, the first line contains an integer , denoting the number of vertices in the polygon . lines follow, line containing two real numbers (with four digit precision after decimal point) denoting the co-ordinate of the vertex of in a counter-clockwise manner.
Sum of across all testcases is less than or equal to .
For each test case, output the minimum total sum of perimeters of and on a single line.
Your output will be considered correct if the absolute or relative error is less than or equal to .
1 3 0.0000 0.0000 1000.0000 0.0000 500.0000 1.0000