Safe Zone

Yeonjong wants to install a new surveillance system in his yard.

There are $N$ circular objects in the yard. Along the boundary of the surveillance system he wants to build a high-voltage fence. The safe zone enclosed by the fence must be connected as a single region, and every object must lie inside this safe zone. No two objects overlap or touch. Write a program that minimizes the total length of the fence under these conditions.

The first line contains the number of test cases $C$ ($0 \le C \le 100$). Each test case begins with a line containing the number of objects $N$ ($0 < N \le 25$). The next $N$ lines each contain three numbers $x_i$, $y_i$, and $r_i$: the $i$-th object is a circle centered at $(x_i, y_i)$ with radius $r_i$ ($|x_i| \le 100$, $|y_i| \le 100$, $0 < r_i \le 100$).

For each test case, print on its own line the minimum length of a fence that encloses all objects, rounded to exactly 10 digits after the decimal point.