3409. Rectilinear polygon

输入格式

The first line of input is an integer giving the number of cases that follow. The input of each case starts with an integer $4\le n\le 100000$ giving the number of points for this test case. It is followed by $n$ pairs of integers specifying the $x$ and $y$ coordinates of the points for this case.

输出格式

The output should contain one line for each case on input. Each line should contain one integer number giving the length of the rectilinear polygon passing throught the given points when it exists; otherwise, it should contain $-1$.

1
8
1 2
1 0
2 1
2 2
3 2
3 1
4 0
4 2

12