Problem Statement

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}

Output

Print all good vertices as integers, in ascending order, using newline as a separator.