Contest Duration: - (local time) (100 minutes) Back to Home
E - Unique Color /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

N 頂点からなる木が与えられます。i 番目の辺は頂点 A_i と頂点 B_i をつないでいます。頂点 i は色 C_i で塗られています (この問題では、色は整数として表されます)。

よい頂点を全て求めてください。

制約

• 2 \leq N \leq 10^5
• 1 \leq C_i \leq 10^5
• 1 \leq A_i,B_i \leq N
• 与えられるグラフは木である
• 入力は全て整数

入力

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


入力例 1

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


出力例 1

1
2
3
4
6


入力例 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


出力例 2

1
2
3
5
6
7
8


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.

Sample Input 1

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


Sample Output 1

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.

Sample Input 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


Sample Output 2

1
2
3
5
6
7
8