Finding Normal

Time Limit: 1 Second    Memory Limit: 32768 KB

Given the coordinates of the vertices of a polygon, find its normal.

Input

The input begins with t, the number of test cases. Each case starts with n (3<= n<= 1000), the number of vertices. It is guaranteed that when viewed from the normal's side, the vertices are given in counter-clockwise order.

Output

For each test case, output the normal in a single line. The normal should be normalized. Round each coordinate to 3 digits after decimal point.

Sample Input

1
3
0 0 0
1 0 0
0 1 0

Sample Output

0.000 0.000 1.000

Submit

Source: ZOJ Monthly, December 2004