Score : $500$ points

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.

6
2 7 1 8 2 8
1 2
3 6
3 2
4 3
2 5

1
2
3
4
6

For example, the shortest path from Vertex $1$ to Vertex $6$ contains Vertices $1,2,3,6$. Among them, only Vertex $6$ itself is painted in the same color as Vertex $6$, so it is a good vertex. On the other hand, the shortest path from Vertex $1$ to Vertex $5$ contains Vertices $1,2,5$, and Vertex $1$ is painted in the same color as Vertex $5$, so Vertex $5$ is not a good vertex.

10
3 1 4 1 5 9 2 6 5 3
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10

1
2
3
5
6
7
8