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Points: 10 (partial)
Time limit: 2.0s
Memory limit: 64M

Problem types

In this problem, you will be required to support the following operations on a forest:

1 u v - Make node u the parent of v if v is a root, and u is not in the subtree of v.

2 u v - Delete the edge between nodes u and v if it exists.

3 u v - Print the highest common ancestor of nodes u and v. If no such node exists, print -1.

There will be Q operations of this form.

However, at most two out of the three operations will appear in any given test case.

Input Specification

The first line will contain one integer N ({1 \le N \le 10^5}).

The next lines will contain N integers p_i ({0 \le p_i \le N}), the parent of node i.

Nodes with parent 0 are roots.

The next line will contain one integer Q ({1 \le Q \le 10^5}).

The next Q lines will contain one query described above.

Output Specification

The answers to the queries, each on one line in the order of the queries.

Sample Input

0 0 1
3 1 1
3 1 2
3 1 3
1 1 2
3 1 2

Sample Output



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