ABland Yard

AtCoder

IDagc027_c

Time2000ms

Memory256MB

Difficulty—

You are given an undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$. In addition, each vertex has a label, `A` or `B`. The label of Vertex $i$ is $s_i$. Edge $i$ bidirectionally connects vertex $a_i$ and $b_i$. The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times. Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint. For example, in a graph where Vertex $1$ has the label `A` and Vertex $2$ has the label `B`, if Nusook travels along the path $1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2$, the resulting string is `ABABB`. Determine if Nusook can make all strings consisting of `A` and `B`. ## Constraints * $2 \leq N \leq 2 \times 10^{5}$ * $1 \leq M \leq 2 \times 10^{5}$ * $|s| = N$ * $s_i$ is `A` or `B`. * $1 \leq a_i, b_i \leq N$ * The given graph may NOT be simple or connected. ## Input Input is given from Standard Input in the following format: $N$ $M$ $s$ $a_1$ $b_1$ $:$ $a_{M}$ $b_{M}$ [samples]

Samples

Input #1

Output #1

Yes

*   Since Nusook can visit Vertex $1$ and Vertex $2$ in any way he likes, he can make all strings consisting of `A` and `B`.

![image](https://img.atcoder.jp/agc027/77e96cf8e213d606ddd8f3c3f8315d32.png)

Input #2

Output #2

No

*   For example, Nusook cannot make `BB`.
*   The given graph may not be connected.

![image](https://img.atcoder.jp/agc027/1ab1411cb9d6ee023d14ca4e77c4b584.png)

Input #3

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9

Output #3

Yes

Input #4

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "ABland Yard",
    "description": {
      "content": "You are given an undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$. In addition, each vertex has a label, `A` or `B",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc027_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an undirected graph consisting of $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$. In addition, each vertex has a label, `A` or `B...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments