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 ≤ 105) - the number of vertices in the graph. The following line contains n integer numbers, i-th number is nexti (0 ≤ nexti ≤ n), meaning that there is an edge from vertex i to vertex nexti. If nexti = 0, assume that there is no outgoing edge from vertex i. Third line contains a natural number m (m ≤ 105) - 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.