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.

Input is given from Standard Input in the following format:

```
$N$
$C_1$ $\ldots$ $C_N$
$A_1$ $B_1$
$\vdots$
$A_{N-1}$ $B_{N-1}$
```

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

-   $2 \leq N \leq 10^5$
-   $1 \leq C_i \leq 10^5$
-   $1 \leq A_i,B_i \leq N$
-   The given graph is a tree.
-   All values in input are integers.

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.