Clique Connect

AtCoder

IDabc352_e

Time2000ms

Memory256MB

Difficulty—

You are given a weighted undirected graph $G$ with $N$ vertices, numbered $1$ to $N$. Initially, $G$ has no edges. You will perform $M$ operations to add edges to $G$. The $i$\-th operation $(1 \leq i \leq M)$ is as follows: * You are given a subset of vertices $S_i=\lbrace A_{i,1},A_{i,2},\dots,A_{i,K_i}\rbrace$ consisting of $K_i$ vertices. For every pair $u, v$ such that $u, v \in S_i$ and $u < v$, add an edge between vertices $u$ and $v$ with weight $C_i$. After performing all $M$ operations, determine whether $G$ is connected. If it is, find the total weight of the edges in a minimum spanning tree of $G$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq 2 \times 10^5$ * $2 \leq K_i \leq N$ * $\sum_{i=1}^{M} K_i \leq 4 \times 10^5$ * $1 \leq A_{i,1} < A_{i,2} < \dots < A_{i,K_i} \leq N$ * $1 \leq C_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $K_1$ $C_1$ $A_{1,1}$ $A_{1,2}$ $\dots$ $A_{1,K_1}$ $K_2$ $C_2$ $A_{2,1}$ $A_{2,2}$ $\dots$ $A_{2,K_2}$ $\vdots$ $K_M$ $C_M$ $A_{M,1}$ $A_{M,2}$ $\dots$ $A_{M,K_M}$ [samples]

Samples

Input #1

Output #1

9

![image](https://img.atcoder.jp/abc352/b54e4b0cfe2f7e5974a2b95be370953a.png)
The left diagram shows $G$ after all $M$ operations, and the right diagram shows a minimum spanning tree of $G$ (the numbers next to the edges indicate their weights).
The total weight of the edges in the minimum spanning tree is $3 + 2 + 4 = 9$.

Input #2

Output #2

\-1

$G$ is not connected even after all $M$ operations.

Input #3

10 5
6 158260522
1 3 6 8 9 10
10 877914575
1 2 3 4 5 6 7 8 9 10
4 602436426
2 6 7 9
6 24979445
2 3 4 5 8 10
4 861648772
2 4 8 9

Output #3

1202115217

API Response (JSON)

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    "name": "Clique Connect",
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      "content": "You are given a weighted undirected graph $G$ with $N$ vertices, numbered $1$ to $N$. Initially, $G$ has no edges. You will perform $M$ operations to add edges to $G$. The $i$\\-th operation $(1 \\leq i",
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a weighted undirected graph $G$ with $N$ vertices, numbered $1$ to $N$. Initially, $G$ has no edges.\nYou will perform $M$ operations to add edges to $G$. The $i$\\-th operation $(1 \\leq i...",
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