Reversi

AtCoder

IDarc143_e

Time2000ms

Memory256MB

Difficulty—

We have a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\-th edge connects Vertex $A_i$ and Vertex $B_i$. Additionally, each vertex has a reversi piece on it. The status of the piece on each vertex is given by a string $S$: if the $i$\-th character of $S$ is `B`, the piece on Vertex $i$ is placed with the black side up; if the $i$\-th character of $S$ is `W`, the piece on Vertex $i$ is placed with the white side up. Determine whether it is possible to perform the operation below $N$ times to remove the pieces from all vertices. If it is possible, find the lexicographically smallest possible sequence $P_1, P_2, \ldots, P_N$ such that Vertices $P_1, P_2, \ldots, P_N$ can be chosen in this order during the process. * Choose a vertex containing a piece with the white side up, and remove the piece from that vertex. Then, flip all pieces on the vertices adjacent to that vertex. Notes on reversi pieces A reversi piece has a black side and a white side, and flipping it changes which side faces up. What is the lexicographical order on sequences?The following is an algorithm to determine the lexicographical order between different sequences $S$ and $T$. Below, let $S_i$ denote the $i$\-th element of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$. 1. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same. 2. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ is less than $T_j$ (as a number), we determine that $S \lt T$ and quit; if $S_j$ is greater than $T_j$, we determine that $S \gt T$ and quit. 3. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq A_i, B_i \leq N$ * The given graph is a tree. * $S$ is a string of length $N$ consisting of the characters `B` and `W`. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ $S$ [samples]

Samples

Input #1

4
1 2
2 3
3 4
WBWW

Output #1

1 2 4 3

Input #2

4
1 2
2 3
3 4
BBBB

Output #2

\-1

In this case, you cannot perform the operation at all.

API Response (JSON)

{
  "problem": {
    "name": "Reversi",
    "description": {
      "content": "We have a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Additionally, each vertex has a reversi piece on it. The status of ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc143_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Additionally, each vertex has a reversi piece on it. The status of ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments