Three Circuits

AtCoder

IDagc032_c

Time2000ms

Memory256MB

Difficulty—

You are given a simple connected undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$. Edge $i$ connects Vertex $a_i$ and $b_i$ bidirectionally. Determine if three circuits (see Notes) can be formed using each of the edges exactly once. ## Constraints * All values in input are integers. * $1 \leq N,M \leq 10^{5}$ * $1 \leq a_i, b_i \leq N$ * The given graph is simple and connected. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $:$ $a_M$ $b_M$ [samples] ## Notes A circuit is a cycle allowing repetitions of vertices but not edges.

Samples

Input #1

Output #1

Yes

*   Three circuits can be formed using each of the edges exactly once, as follows:
    
    ![image](https://img.atcoder.jp/agc031/b8c8e2245d45a31cf39749b0a49fc2bd.png)

Input #2

Output #2

No

*   Three circuits are needed.

Input #3

Output #3

Yes

API Response (JSON)

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  "problem": {
    "name": "Three Circuits",
    "description": {
      "content": "You are given a simple connected undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$. Edge $i$ connects Vertex $a_i$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc032_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple connected undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$.\nEdge $i$ connects Vertex $a_i$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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