3 Steps

AtCoder

IDcode_festival_2017_qualb_c

Time2000ms

Memory256MB

Difficulty—

Rng has a connected undirected graph with $N$ vertices. Currently, there are $M$ edges in the graph, and the $i$\-th edge connects Vertices $A_i$ and $B_i$. Rng will add new edges to the graph by repeating the following operation: * Operation: Choose $u$ and $v$ $(u \neq v)$ such that Vertex $v$ can be reached by traversing exactly three edges from Vertex $u$, and add an edge connecting Vertices $u$ and $v$. It is not allowed to add an edge if there is already an edge connecting Vertices $u$ and $v$. Find the maximum possible number of edges that can be added. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq A_i,B_i \leq N$ * The graph has no self-loops or multiple edges. * The graph is connected. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

4

If we add edges as shown below, four edges can be added, and no more.
![image](https://img.atcoder.jp/code-festival-2017-qualb/6e99dccc06ac8b14d9ca2e297524bc0c.png)

Input #2

Output #2

5

Five edges can be added, for example, as follows:

*   Add an edge connecting Vertex $5$ and Vertex $3$.
*   Add an edge connecting Vertex $5$ and Vertex $2$.
*   Add an edge connecting Vertex $4$ and Vertex $1$.
*   Add an edge connecting Vertex $4$ and Vertex $2$.
*   Add an edge connecting Vertex $4$ and Vertex $3$.

API Response (JSON)

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    "name": "3 Steps",
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      "content": "Rng has a connected undirected graph with $N$ vertices. Currently, there are $M$ edges in the graph, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$. Rng will add new edges to the graph by repe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "code_festival_2017_qualb_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Rng has a connected undirected graph with $N$ vertices. Currently, there are $M$ edges in the graph, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$.\nRng will add new edges to the graph by repe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments