Preserve Diameter

AtCoder

IDhitachi2020_f

Time4000ms

Memory256MB

Difficulty—

We have a tree $G$ with $N$ vertices numbered $1$ to $N$. The $i$\-th edge of $G$ connects Vertex $a_i$ and Vertex $b_i$. Consider adding zero or more edges in $G$, and let $H$ be the graph resulted. Find the number of graphs $H$ that satisfy the following conditions, modulo $998244353$. * $H$ does not contain self-loops or multiple edges. * The diameters of $G$ and $H$ are equal. * For every pair of vertices in $H$ that is not directly connected by an edge, the addition of an edge directly connecting them would reduce the diameter of the graph. ## Constraints * $3 \le N \le 2 \times 10^5$ * $1 \le a_i, b_i \le N$ * The given graph is a tree. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $\vdots$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

3

For example, adding the edges $(1, 5), (3, 5)$ in $G$ satisfies the conditions.

Input #2

3
1 2
2 3

Output #2

1

The only graph $H$ that satisfies the conditions is $G$.

Input #3

Output #3

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Preserve Diameter",
    "description": {
      "content": "We have a tree $G$ with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of $G$ connects Vertex $a_i$ and Vertex $b_i$. Consider adding zero or more edges in $G$, and let $H$ be the graph resulted. ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "hitachi2020_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree $G$ with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of $G$ connects Vertex $a_i$ and Vertex $b_i$.\nConsider adding zero or more edges in $G$, and let $H$ be the graph resulted.\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments