Unique Color

Given 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 for Vertex $x$ itself.

Find all the good vertices.

Input

The first line contains the number of vertices $n(2\le n\le 10^5)$. The second line contains colors $c_1,c_2,...,c_n(1\le c_i\le 10^5)$. Each of the next $n-1$ lines contains two integers $a_i$ and $b_i(1\le a_i,b_i\le n)$.

Output

Print all good vertices as integers, in ascending order. Print each number on a separate line.

Examples