X Property

The X property is a property of two intersected circles. Suppose we have two intersected circls P and Q, and they intersect at A and B. If the two circles satisfy:

AP*BQ+AQ*BP=AB*PQ

we call these two circles satisfy the X property.

Given N circles on a plane, can you find a circle which has X property with all the N given circles?

The first line comes an integer T (T<=20), indicating there are T test cases. For each case, there will be an integer N (1<=N<=100000) in the first line. Then comes N lines. Each of them contains three integer numbers X_i, Y_i, R_i (-1000000<=X_i, Y_i<=1000000, 0<R_i<=1000000) representing the center of the ith circle and the radius of it.

For each case print one line. If there is exactly one such circle, output its center coordinates and radius as real numbers separated with single spaces. The numbers will be considered correct if they are within 10-6 relative or absolute error of the exact answers.

If there is no such circles, print -1. If there are more than one such circles, print -2.

3
3 
0 0 1 
2 0 1 
1 3 1 
2
0 0 1
1 1 2
3
0 1 1
0 -1 1
-1 0 1

1.000000 1.333333 1.333333
-2
-1

2011 Multi-University Training Contest 4 - Host by SDU