Shortest Fence

Your garden holds trees and goats. To keep the goats off the trees you decide to build one fence that encloses every tree, and you want that fence to be as short as possible.

Seen from above, each tree is a circle in the plane. The fence is a closed curve that keeps every tree inside it, and it touches some or all of the trees. Find the smallest possible length of such a fence.

The first line contains the number of test cases $T$. ($1 \le T \le 250$)

Each test case is given in $N + 1$ lines. The first line contains the number of trees in the garden $N$. ($1 \le N \le 100$) Each of the next $N$ lines contains three integers $X$, $Y$ and $R$ separated by spaces. $X$ and $Y$ are the coordinates of the centre of a tree and $R$ is its radius.

$X$, $Y$ and $R$ are integers between $1$ and $1000$, inclusive. No two trees in the input touch or overlap.

For each test case, print on one line the minimum length of a fence that surrounds every tree. Round the value at the sixth decimal place and always print five digits after the decimal point.