{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eLet $$$G$$$ and $$$H$$$ be two weighted undirected simple graphs. We define the \u003cspan class\u003d\"tex-font-style-it\"\u003ecartesian product\u003c/span\u003e of the two graphs, $$$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)$$$ if and only if:\u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$v_1 \u003d v_2$$$ and there is an edge $$$(u_1, u_2)$$$ in $$$G$$$. In this case, the edge$$$((u_1, v_1), (u_2, v_2))$$$ in $$$G \\square H$$$ has the same weight as the edge $$$(u_1, u_2)$$$ in $$$G$$$. \u003c/li\u003e\u003cli\u003e or $$$u_1 \u003d u_2$$$ and there is an edge $$$(v_1, v_2)$$$ in $$$H$$$. In this case, the edge$$$((u_1, v_1), (u_2, v_2))$$$ in $$$G \\square H$$$ has the same weight as the edge $$$(v_1, v_2)$$$ in $$$H$$$. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYou are given two connected graphs $$$G$$$ and $$$H$$$. Compute the total weight of the minimum spanning tree of $$$G \\square H$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains four integers $$$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$$$, respectively. \u003c/p\u003e\u003cp\u003eEach of the next $$$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$$$.\u003c/p\u003e\u003cp\u003eEach of the next $$$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$$$.\u003c/p\u003e\u003cp\u003eIt is guaranteed that graphs $$$G$$$ and $$$H$$$ are simple and connected. Recall that a graph is \u003cspan class\u003d\"tex-font-style-it\"\u003esimple\u003c/span\u003e if there are no edges between a vertex and itself, and there is at most one edge between any two vertices.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput one integer: the weight of the minimum spanning tree of $$$G \\square H$$$.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 4 3 2\n0 1 3\n1 2 2\n2 3 2\n3 0 5\n0 1 1\n1 2 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e15\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}