Problems
Unique Color
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 data
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 data
Print all good vertices as integers, in ascending order. Print each number on a separate line.
Examples
Input example #1
6 2 7 1 8 2 8 1 2 3 6 3 2 4 3 2 5
Output example #1
1 2 3 4 6
Input example #2
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
Output example #2
1 2 3 5 6 7 8