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Average distance

Time Limit: 2 Seconds      Memory Limit: 65536 KB      Special Judge

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

8.6

Source: The 2007 Benelux Algorithm Programming Contest
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