Black Radius

AtCoder

IDagc008_f

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices. The vertices are numbered $1$ through $N$. For each $1 ≤ i ≤ N - 1$, the $i$\-th edge connects vertices $a_i$ and $b_i$. The lengths of all the edges are $1$. Snuke likes some of the vertices. The information on his favorite vertices are given to you as a string $s$ of length $N$. For each $1 ≤ i ≤ N$, $s_i$ is `1` if Snuke likes vertex $i$, and `0` if he does not like vertex $i$. Initially, all the vertices are white. Snuke will perform the following operation exactly once: * Select a vertex $v$ that he likes, and a non-negative integer $d$. Then, paint all the vertices black whose distances from $v$ are at most $d$. Find the number of the possible combinations of colors of the vertices after the operation. ## Constraints * $2 ≤ N ≤ 2×10^5$ * $1 ≤ a_i, b_i ≤ N$ * The given graph is a tree. * $|s| = N$ * $s$ consists of `0` and `1`. * $s$ contains at least one occurrence of `1`. ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $a_2$ $b_2$ $:$ $a_{N - 1}$ $b_{N - 1}$ $s$ ## Partial Score * In the test set worth $1300$ points, $s$ consists only of `1`. [samples]

Samples

Input #1

Output #1

4

The following four combinations of colors of the vertices are possible:

![image](https://atcoder.jp/img/agc008/334d566ec1f4f38d23cd580044f1cd07.png)

Input #2

Output #2

11

This case satisfies the additional constraint for the partial score.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Black Radius",
    "description": {
      "content": "There is a tree with $N$ vertices. The vertices are numbered $1$ through $N$. For each $1 ≤ i ≤ N - 1$, the $i$\\-th edge connects vertices $a_i$ and $b_i$. The lengths of all the edges are $1$. Snuke ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc008_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices. The vertices are numbered $1$ through $N$. For each $1 ≤ i ≤ N - 1$, the $i$\\-th edge connects vertices $a_i$ and $b_i$. The lengths of all the edges are $1$.\nSnuke ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments