Note: This is an approximate problem. There is no exact solution. You must find the most optimal solution. Please, take a look at the sample explanation to ensure that you understand the problem correctly.

Problem statement

Given a connected network G with N Railway Stations and M Railway Tracks. Each track connects two different Railway Stations and has a cost C associated with it.

We have a set S consisting of Railway Stations in G. |S| = K .

We need to find a network T, which is a subnetwork of G and has all stations present in set S. (It is possible that T has some stations not present in S). In T , there must exists a unique path between any two stations.

We need to select T such that (Z = Sum of costs of Tracks present in T) is minimized.

Input format :

First line contains two space-separated integers : N and M
Next M lines contain three space separated integers U V W, denoting a track between station U and V with cost W.
Next line contain an integer K
Next line contain K space separated integers, denoting set S.

Output format :

In first line print E, number of edges in T
In next line print E space separated integers denoting the index of edges 1 - based (as per the Input) present in T.

Verdict and scoring :

Your score is equal to the sum of the values of all test files. The value of each test file is equal to the value of Z that you found.

If T is invalid or T does not has all stations present in S then you will recieve a Wrong Answer Verdict.

Constraints :

\(N = 100000, M = 1000000\)
\(5000 <= K <= 10000\)
\(1 <= W <= 100000\)