308207: CF1482F. Useful Edges

You are given a weighted undirected graph on $n$ vertices along with $q$ triples $(u, v, l)$, where in each triple $u$ and $v$ are vertices and $l$ is a positive integer. An edge $e$ is called useful if there is at least one triple $(u, v, l)$ and a path (not necessarily simple) with the following properties:

• $u$ and $v$ are the endpoints of this path,
• $e$ is one of the edges of this path,
• the sum of weights of all edges on this path doesn't exceed $l$.

Please print the number of useful edges in this graph.

The first line contains two integers $n$ and $m$ ($2\leq n\leq 600$, $0\leq m\leq \frac{n(n-1)}2$).

Each of the following $m$ lines contains three integers $u$, $v$ and $w$ ($1\leq u, v\leq n$, $u\neq v$, $1\leq w\leq 10^9$), denoting an edge connecting vertices $u$ and $v$ and having a weight $w$.

The following line contains the only integer $q$ ($1\leq q\leq \frac{n(n-1)}2$) denoting the number of triples.

Each of the following $q$ lines contains three integers $u$, $v$ and $l$ ($1\leq u, v\leq n$, $u\neq v$, $1\leq l\leq 10^9$) denoting a triple $(u, v, l)$.

It's guaranteed that:

• the graph doesn't contain loops or multiple edges;
• all pairs $(u, v)$ in the triples are also different.

Print a single integer denoting the number of useful edges in the graph.

4 6
1 2 1
2 3 1
3 4 1
1 3 3
2 4 3
1 4 5
1
1 4 4

5

4 2
1 2 10
3 4 10
6
1 2 11
1 3 11
1 4 11
2 3 11
2 4 11
3 4 9

1

3 2
1 2 1
2 3 2
1
1 2 5

2

In the first example each edge is useful, except the one of weight $5$.

In the second example only edge between $1$ and $2$ is useful, because it belongs to the path $1-2$, and $10 \leq 11$. The edge between $3$ and $4$, on the other hand, is not useful.

In the third example both edges are useful, for there is a path $1-2-3-2$ of length exactly $5$. Please note that the path may pass through a vertex more than once.