Unique Color

AtCoder

IDabc198_e

Time2000ms

Memory256MB

Difficulty—

Given is a tree with $N$ vertices numbered $1$ through $N$. The $i$\-th edge connects Vertex $A_i$ and Vertex $B_i$. Vertex $i$ is painted in color $C_i$ (in this problem, colors are represented as integers). Vertex $x$ is said to be **good** when the shortest path from Vertex $1$ to Vertex $x$ does not contain a vertex painted in the same color as Vertex $x$, except Vertex $x$ itself. Find all good vertices. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq C_i \leq 10^5$ * $1 \leq A_i,B_i \leq N$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $C_1$ $\ldots$ $C_N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ [samples]

Samples

Input #1

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

Output #1

1
2
3
4
6

For example, the shortest path from Vertex $1$ to Vertex $6$ contains Vertices $1,2,3,6$. Among them, only Vertex $6$ itself is painted in the same color as Vertex $6$, so it is a good vertex.  
On the other hand, the shortest path from Vertex $1$ to Vertex $5$ contains Vertices $1,2,5$, and Vertex $1$ is painted in the same color as Vertex $5$, so Vertex $5$ is not a good vertex.

Input #2

10
3 1 4 1 5 9 2 6 5 3
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Unique Color",
    "description": {
      "content": "Given is a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Vertex $i$ is painted in color $C_i$ (in this problem, colors are represented as in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc198_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Vertex $i$ is painted in color $C_i$ (in this problem, colors are represented as in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments