You are given a rooted tree consisting of  vertices numbered from  to  and vertex  is the root of the tree. The depth of vertex  is .

A tree is a connected undirected graph with  edges.

Now there are  tasks that you need to do, and the -th task is one of the following three types:

•     --- Add a new vertex numbered  between vertex  and its parent vertex.

•     --- Delete the vertex  and turn all child vertex of  into the child vertex of its parent vertex.
•     --- Query the depth of the vertex .

It is guaranteed that the vertex  must exist in the current tree.

输入描述:

The first line of the input contains two integers  .

The second line contains  integers  --- the parents of vertices from the second to the -th .

The next  lines each line contains two integers, and the -th line belongs to one of the three types mentioned above.

It is guaranteed that there has  query task.

输出描述:

For each query task, you should output one line containing an integer.

6 5
1 1 3 3 3
3 4
1 3
3 4
2 3
3 4

3
4
3