Tree and queries 5

You are given a tree with $N$ vertices. A tree is a connected undirected graph with no cycle. The vertices are numbered from 1 to $N$, and the edges are numbered from 1 to $N-1$. Every vertex is black at the start.

Write a program that handles the two query types below.

• 1 i: flip the color of vertex $i$. Black becomes white, and white becomes black.
• 2 v: among all white vertices $u$, print the smallest distance from $u$ to $v$. Here $u$ and $v$ may be the same vertex, so the answer is 0 when $v$ is white. If the tree has no white vertex, print -1.

The distance between two vertices is the number of edges on the path that joins them.

The first line contains the number of vertices $N$ ($2 \le N \le 100000$).

Each of the next $N-1$ lines contains the two vertex numbers $u$ and $v$ joined by edge $i$ ($1 \le u, v \le N$).

The next line contains the number of queries $M$ ($1 \le M \le 100000$).

Each of the next $M$ lines contains one query, written as 1 i or 2 v, with $1 \le i, v \le N$.

For each query of type 2, print the answer on its own line, in the order the queries are given.