A tree with vertices numbered from to is given. The -th edge of the tree connects vertices a_i and b_i. Vertex is colored with color c_i (in this problem, colors are represented by integers).
A vertex is considered good if the shortest path from vertex to vertex does not contain any other vertex with the same color as vertex , except for itself.
Find all good vertices.
The first line contains an integer (2 \le n \le 10^5) — the number of vertices.
The second line contains integers — the colors of the vertices: c_1, c_2, \ldots, c_n (1 \le c_i \le 10^5).
Each of the following n - 1 lines contains two integers a_i and b_i (1 \le a_i, b_i \le n) — the edges of the tree.
Print all good vertices, one per line, in ascending order of their indices.

Example 1
Example 2