Special graph
You are given a directed graph with n vertices. The special thing about the graph is that each vertex has at most one outgoing edge. Your task is to answer the following two types of queries:
1 a - delete the only edge outgoing from vertex a. It is guaranteed that the edge exists (1 ≤ a ≤ n),
2 a b - output the length of the shortest path from vertex a to vertex b, if the path exists. Otherwise output **-1** without quotes (1 ≤ a, b ≤ n).
Input
First line contains a natural number n (n ≤ 10^5) - the number of vertices in the graph. The following line contains n integer numbers, i-th number is next[i] (0 ≤ next[i] ≤ n), meaning that there is an edge from vertex i to vertex next[i]. If next[i] = 0, assume that there is no outgoing edge from vertex i. Third line contains a natural number m (m ≤ 10^5) - the number of queries. The following m contain a query each. Queries are given in the manner described above.
Output
On the i-th line output the answer for the i-th query of type 2 a b.