Monochrome Cat

AtCoder

IDarc097_d

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices numbered $1$ through $N$. The $i$\-th edge connects Vertex $x_i$ and $y_i$. Each vertex is painted white or black. The initial color of Vertex $i$ is represented by a letter $c_i$. $c_i$ $=$ `W` represents the vertex is white; $c_i$ $=$ `B` represents the vertex is black. A cat will walk along this tree. More specifically, she performs one of the following in one second repeatedly: * Choose a vertex that is adjacent to the vertex where she is currently, and move to that vertex. Then, invert the color of the destination vertex. * Invert the color of the vertex where she is currently. The cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex. At least how many seconds does it takes for the cat to achieve her objective? ## Constraints * $1$ $≤$ $N$ $≤$ $10^5$ * $1$ $≤$ $x_i,y_i$ $≤$ $N$ ($1$ $≤$ $i$ $≤$ $N-1$) * The given graph is a tree. * $c_i$ $=$ `W` or $c_i$ $=$ `B`. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_{N-1}$ $y_{N-1}$ $c_1c_2..c_N$ [samples]

Samples

Input #1

5
1 2
2 3
2 4
4 5
WBBWW

Output #1

5

The objective can be achieved in five seconds, for example, as follows:

*   Start at Vertex $1$. Change the color of Vertex $1$ to black.
*   Move to Vertex $2$, then change the color of Vertex $2$ to white.
*   Change the color of Vertex $2$ to black.
*   Move to Vertex $4$, then change the color of Vertex $4$ to black.
*   Move to Vertex $5$, then change the color of Vertex $5$ to black.

Input #2

6
3 1
4 5
2 6
6 1
3 4
WWBWBB

Output #2

Input #3

1
B

Output #3

Input #4

20
2 19
5 13
6 4
15 6
12 19
13 19
3 11
8 3
3 20
16 13
7 14
3 17
7 8
10 20
11 9
8 18
8 2
10 1
6 13
WBWBWBBWWWBBWWBBBBBW

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Monochrome Cat",
    "description": {
      "content": "There is a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects Vertex $x_i$ and $y_i$. Each vertex is painted white or black. The initial color of Vertex $i$ is represented by a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc097_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices numbered $1$ through $N$. The $i$\\-th edge connects Vertex $x_i$ and $y_i$. Each vertex is painted white or black. The initial color of Vertex $i$ is represented by a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments