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ZOJ Problem Set - 2272
Finding Normal

Time Limit: 2 Seconds      Memory Limit: 65536 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



Author: PAN, Minghao
Source: ZOJ Monthly, December 2004
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