Rainbow Roads

You are given a tree with $n$ nodes, numbered from 1 to $n$. Every edge has one of $n$ colors. A path in the tree is a rainbow path if every two adjacent edges on it have different colors. A node $v$ is good if every simple path that has $v$ as one of its endpoints is a rainbow path.

Find all the good nodes of the given tree.

A simple path is a path that repeats no vertex and no edge.

The first line contains one integer $n$ ($1 \le n \le 50\,000$).

Each of the next $n - 1$ lines contains three integers $a_i$, $b_i$, and $c_i$ separated by spaces ($1 \le a_i, b_i, c_i \le n$, $a_i \ne b_i$). They describe an edge of color $c_i$ that connects node $a_i$ and node $b_i$.

The given edges always form a tree.

On the first line, print $k$, the number of good nodes.

On each of the next $k$ lines, print the index of one good node, in increasing order.

The rainbow condition applies only to consecutive edges of a path. On a path $v_1, v_2, v_3, v_4$ the edges $(v_1, v_2)$ and $(v_3, v_4)$ may share a color, because they are not adjacent. A path with at most one edge has no adjacent pair of edges, so it is always a rainbow path.