Graph

AtCoder

IDasaporo_c

Time3000ms

Memory256MB

Difficulty—

Takahashi found an undirected connected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$. The $i$\-th edge connects vertices $a_i$ and $b_i$, and has a weight of $c_i$. He will play $Q$ rounds of a game using this graph. In the $i$\-th round, two vertices $S_i$ and $T_i$ are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices $S_i$ or $T_i$ by traversing chosen edges. For each round, find the minimum possible total weight of the edges chosen by Takahashi. ## Constraints * $1 ≦ N ≦ 4,000$ * $1 ≦ M ≦ 400,000$ * $1 ≦ Q ≦ 100,000$ * $1 ≦ a_i,b_i,S_i,T_i ≦ N$ * $1 ≦ c_i ≦ 10^{9}$ * $a_i \neq b_i$ * $S_i \neq T_i$ * The given graph is connected. ## Input The input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $c_1$ $a_2$ $b_2$ $c_2$ : $a_M$ $b_M$ $c_M$ $Q$ $S_1$ $T_1$ $S_2$ $T_2$ : $S_Q$ $T_Q$ ## Partial Scores * In the test set worth $200$ points, $Q = 1$. * In the test set worth another $300$ points, $Q ≦ 3000$. [samples]

Samples

Input #1

Output #1

8
7

We will examine each round:

*   In the $1$\-st round, choosing edges $1$ and $3$ achieves the minimum total weight of $8$.
*   In the $2$\-nd round, choosing edges $1$ and $2$ achieves the minimum total weight of $7$.

Input #2

Output #2

8

This input satisfies the additional constraints for both partial scores.

API Response (JSON)

{
  "problem": {
    "name": "Graph",
    "description": {
      "content": "Takahashi found an undirected connected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$. The $i$\\-th edge connects vertices $a_i$ and $b_i$, and has a weight of $c_i$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "asaporo_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi found an undirected connected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$. The $i$\\-th edge connects vertices $a_i$ and $b_i$, and has a weight of $c_i$....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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