You are given a tree with n nodes (conveniently numbered from 1 to n). Each edge in this tree has one of n colors. A path in this tree is called a rainbow if all adjacent edges in the path have different colors. Also, a node is called good if every simple path with that node as one of its endpoints is a rainbow path.</p>

Find all the good nodes in the given tree.

A simple path is a path that does not repeat any vertex or edge.

입력 형식

The first line of input contains a single integer n (1 ≤ n ≤ 50,000).</p>

Each of the next n − 1 lines contains three space-separated integers a_i, b_i, and c_i (1 ≤ a_i, b_i, c_i ≤ n; a_i ≠ b_i), describing an edge of color c_i that connects nodes a_i and b_i.

It is guaranteed that the given edges form a tree.

출력 형식

On the first line of the output, print k, the number of good nodes.</p>

In the next k lines, print the indices of all good nodes in numerical order, one per line.

예제 입력 1

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

예제 출력 1

4
3
4
5
6

예제 입력 2

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

예제 출력 2

0

예제 입력 3

9
1 2 2
1 3 1
1 4 5
1 5 5
2 6 3
3 7 3
4 8 1
5 9 2

예제 출력 3

5
1
2
3
6
7

예제 입력 4

10
9 2 1
9 3 1
9 4 2
9 5 2
9 1 3
9 6 4
1 8 5
1 10 5
6 7 9

예제 출력 4

4
1
6
7
9

힌트

For the first sample, node 3 is good since all paths that have node 3 as an endpoint are rainbow. In particular, even though the path 3—4—5—6 has two edges of the same color (i.e. 3—4, 5—6), it is still rainbow since these edges are not adjacent.