Let $$$G$$$ and $$$H$$$ be two weighted undirected simple graphs. We define the cartesian product of the two graphs, $$$G \square H$$$, as the graph whose vertex set is the cartesian set product of the vertex sets of the two graphs $$$V(G) \times V(H)$$$ and in which there is an edge between vertices $$$(u_1, v_1)$$$ and $$$(u_2, v_2)$$$ if and only if:
You are given two connected graphs $$$G$$$ and $$$H$$$. Compute the total weight of the minimum spanning tree of $$$G \square H$$$.
The first line contains four integers $$$n_1, m_1, n_2, m_2$$$ ($$$2 \leq n_1, n_2 \leq 10^5$$$; $$$1 \leq m_1, m_2 \leq 10^5$$$): the number of vertices of $$$G$$$, the number of edges of $$$G$$$, the number of vertices of $$$H$$$, and the number of edges of $$$H$$$, respectively.
Each of the next $$$m_1$$$ lines contains three integers $$$u_i, v_i, w_i$$$ ($$$0 \leq u_i, v_i \leq n_1 - 1$$$; $$$1 \leq w_i \leq 10^8$$$), describing an edge of $$$G$$$ between vertices $$$u_i$$$ and $$$v_i$$$ with weight $$$w_i$$$.
Each of the next $$$m_2$$$ lines contains three integers $$$u_i, v_i, w_i$$$ ($$$0 \leq u_i, v_i \leq n_2 - 1$$$; $$$1 \leq w_i \leq 10^8$$$), describing an edge of $$$H$$$ between vertices $$$u_i$$$ and $$$v_i$$$ with weight $$$w_i$$$.
It is guaranteed that graphs $$$G$$$ and $$$H$$$ are simple and connected. Recall that a graph is simple if there are no edges between a vertex and itself, and there is at most one edge between any two vertices.
Output one integer: the weight of the minimum spanning tree of $$$G \square H$$$.
4 4 3 2 0 1 3 1 2 2 2 3 2 3 0 5 0 1 1 1 2 1
15
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