SP9123 GCPC11G - Security Zone

The manager of a large security company has to build a new surveillance system for different sites. A site consists of _N_ objects where each object has its own security circle. At the border of the surveillance system a high voltage fence has to be installed. The security zone inside of the fence has to be connected. Furthermore, all objects and their security circles should be inside the security zone. The security circles of different objects will never overlap or touch. Now the manager needs your help. He asks you for the minimal needed fence length. 

The first line of the input gives the number of test cases _C_ (_0 ). The first line of each such test case holds the integer _N_: the number of objects in the current site (_0 < N ). Each of the following _N_ lines holds three integers _x $ _{i} $_ , _y $ _{i} $_ , and _r $ _{i} $_ that describe an object. The coordinates of the i-th object and the radius for the needed security circle for this object. (|_x $ _{i} $_ |,|_y $ _{i} $_ | 100_, _0 < r $ _{i} $ ) (The center of the security circle around an object is the position of the object itself.)__

For each test case print one line containing the minimal fence length for this case. Your output should have an absolute or relative error of at most _10 $ ^{-7} $_ .