Description:
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.
Input Format:
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.
Output Format:
Print a single integer denoting the number of useful edges in the graph.
Note:
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.