Alice is interesting in computation geometry problem recently. She found a interesting problem and solved it easily. Now she will give this problem to you :
You are given N distinct points (X_i,Y_i) on the two-dimensional plane. Your task is to find a point P and a real number R, such that for at least given points, their distance to point P is equal to R.

输入描述:

The first line is the number of test cases.
For each test case, the first line contains one positive number N(1 ≤ N ≤ 105).
The following N lines describe the points. Each line contains two real numbers Xi and Yi (0 ≤ |Xi|, |Yi| ≤ 103) indicating one give point. It's guaranteed that N points are distinct.

输出描述:

For each test case, output a single line with three real numbers XP, YP, R, where (XP,YP) is the coordinate of required point P. Three real numbers you output should satisfy 0 ≤ |XP|, |YP|, R ≤ 109.
It is guaranteed that there exists at least one solution satisfying all conditions. And if there are different solutions, print any one of them. The judge will regard two point's distance as R if it is within an absolute error of 10-3 of R.

1
7
1 1
1 0
1 -1
0 1
-1 1
0 -1
-1 0

0 0 1