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

3
0 0 1
5
3 1 1
3 1 2
3 1 3
1 1 2
3 1 2

Sample Output

1
-1
1
1