Koothrappali is hungry and it's almost dinner time. So, he must find a good place to have dinner. He has this weird habit of having dinner at two different places and then comparing which one was better. He has located N restaurants near him from which he'll choose two places to have dinner. These N restaurants are connected by N - 1 roads and one can reach one restaurant from another using a combination of these roads.
Since he is an introvert, he doesn't want to travel much between restaurants. He has chosen X restaurants out of these N restaurants. Now, he'll choose two restaurants randomly from these X restaurants. He has asked you to find the expected value of distance between the chosen two restaurants. Can you help him?
Input Format:
First line consists of N, number of restaurants.
Each of the next N - 1 lines consists of 3 integers U, V and W, denoting that there is a road of length W between restaurants U and V.
Next line contains a single integer Q, number of queries.
Each of the next Q lines contain an integer X followed by X integers denoting the restaurants chosen by Koothrappali.
Output Format:
For each query, output the required expected value in form of an irreducible fraction P/Q, that is, gcd(P, Q) must be equal to 1.
Constraints:
2≤N≤105
1≤U,V≤N
1≤W≤105
1≤Q≤10
2≤X≤N
For first query, there is only one pair possible, that is, restaurant 1 to restaurant 4 with length of 6 units.
For second query, there are 3 pairs possible with path length equal to 2, 3, and 5. Hence, expected value is 10/3.
For third query, there are 10 pairs possible with path lengths equal to 2, 3, 6, 7, 5, 4, 5, 9, 10, 9. Hence, expected value is 6/1.
