Problem Statement

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 $S \gt T$. 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. 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. 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

Output

If the objective is unachievable, print -1. If it is achievable, print the answer in the following format:

P_1 P_2 \cdots P_N