Special graph

You are given a directed graph with $N$ vertices. The graph is special because every vertex has at most one outgoing edge. Process two kinds of queries.

• 1 a: delete the edge going out of vertex $a$. This edge is guaranteed to exist.
• 2 a b: print the length of the shortest path from vertex $a$ to vertex $b$. If there is no such path, print -1.

The length of a path is the number of edges on it. Since a vertex has at most one outgoing edge, only one walk starts at $a$, and the answer is the number of edges you follow along that walk until you first reach $b$. If $a$ and $b$ are the same, the answer is 0.

The first line contains the number of vertices $N$ ($1 \le N \le 10^5$).

The second line contains $N$ integers $next_1, next_2, \dots, next_N$ ($0 \le next_i \le N$). The value $next_i$ means there is an edge from vertex $i$ to vertex $next_i$. If $next_i = 0$, vertex $i$ has no outgoing edge.

The third line contains the number of queries $M$ ($1 \le M \le 10^5$).

Each of the next $M$ lines contains one query in the format described above, with $1 \le a, b \le N$.

For each 2 a b query, print one answer per line, in the order the queries are given.