path pass i

AtCoder

IDabc163_f

Time2000ms

Memory256MB

Difficulty—

We have a tree with $N$ vertices numbered $1$ to $N$. The $i$\-th edge in this tree connects Vertex $a_i$ and $b_i$. Additionally, each vertex is painted in a color, and the color of Vertex $i$ is $c_i$. Here, the color of each vertex is represented by an integer between $1$ and $N$ (inclusive). The same integer corresponds to the same color; different integers correspond to different colors. For each $k=1, 2, ..., N$, solve the following problem: * Find the number of simple paths that visit a vertex painted in the color $k$ one or more times. **Note:** The simple paths from Vertex $u$ to $v$ and from $v$ to $u$ are not distinguished. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq c_i \leq N$ * $1 \leq a_i,b_i \leq N$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $c_1$ $c_2$ $...$ $c_N$ $a_1$ $b_1$ $:$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

5
4
0

Let $P_{i,j}$ denote the simple path connecting Vertex $i$ and $j$.
There are $5$ simple paths that visit a vertex painted in the color $1$ one or more times:  
$P_{1,1}\,,\,$ $P_{1,2}\,,\,$ $P_{1,3}\,,\,$ $P_{2,3}\,,\,$ $P_{3,3}$
There are $4$ simple paths that visit a vertex painted in the color $2$ one or more times:  
$P_{1,2}\,,\,$ $P_{1,3}\,,\,$ $P_{2,2}\,,\,$ $P_{2,3}$
There are no simple paths that visit a vertex painted in the color $3$ one or more times.

Input #2

1
1

Output #2

Input #3

2
1 2
1 2

Output #3

2
2

Input #4

Output #4

Input #5

8
2 7 2 5 4 1 7 5
3 1
1 2
2 7
4 5
5 6
6 8
7 8

Output #5

API Response (JSON)

{
  "problem": {
    "name": "path pass i",
    "description": {
      "content": "We have a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and $b_i$. Additionally, each vertex is painted in a color, and the color of Vertex $i$ is $c_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc163_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and $b_i$. Additionally, each vertex is painted in a color, and the color of Vertex $i$ is $c_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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