```Description

Given a tree, calculate the average distance between two vertices in the tree. For example,
the average distance between two vertices in the following tree is (d01 + d02 + d03 + d04 +
d12 +d13 +d14 +d23 +d24 +d34)/10 = (6+3+7+9+9+13+15+10+12+2)/10 = 8.6.

Input

On the first line an integer t (1 <= t <= 100): the number of test cases. Then for each test
case:
* One line with an integer n (2 <= n <= 10 000): the number of nodes in the tree. The
nodes are numbered from 0 to n - 1.
* n - 1 lines, each with three integers a (0 <= a < n), b (0 <= b < n) and d (1 <= d <=
1 000). There is an edge between the nodes with numbers a and b of length d. The
resulting graph will be a tree.

Output

For each testcase:
* One line with the average distance between two vertices. This value should have
either an absolute or a relative error of at most 10^(-3).

Sample Input

1
5
0 1 6
0 2 3
0 3 7
3 4 2

Sample Output

8.600

Source

Benelux Algorithm Programming Contest
October 27, 2007

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