Weighted points

You have N points on 2-d plane. Coordinates of each point P_i are (x_i, y_i). Each point has a weight w_i associated with it. Given a point X, we define the distance function F as

Here D(X,P_i) denotes the Euclidean distance between X and point P_i.

Find a point X such that distance function F(x) is minimized. Output the minimum value of F(x).

Input

First line contains T, the number of test cases. First line of each test case contains N, the number of points. Each of the next N lines contains three space separated integers x_i, y_i and w_i respectively.

It is known that T ≤ 20, N ≤ 1000, 0 ≤ x_i, y_i, w_i ≤ 1000.

Output

Output contains T lines, each containing minimum value of F(x) rounded to 3 decimal places.

Examples