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F. Useful Edges

time limit per test

5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou 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

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

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

Examples

Input

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

Output

5

Input

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

Output

1

Input

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

Output

2

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.

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