You are given a tree (an acyclic undirected connected graph) with N nodes. The tree nodes are numbered from 1 to N. We define dist(a, b) as the number of edges on the path from node a to node b.

Each node has a color, white or black. All the nodes are black initially.

We will ask you to perform some instructions of the following form:

• 0 i : change the color of i-th node(from black to white, or from white to black).
• 1 v : ask for the minimum dist(u, v), node u must be white(u can be equal to v). Obviously, as long as node v is white, the result will always be 0.

Input

• In the first line there is an integer N (N <= 100000)
• In the next N-1 lines, the i-th line describes the i-th edge: a line with two integers a b denotes an edge between a and b.
• In the next line, there is an integer Q denotes the number of instructions (Q <= 100000)
• In the next Q lines, each line contains an instruction "0 i" or "1 v"

Output

For each "1 v" operation, print one integer representing its result. If there is no white node in the tree, you should write "-1".

Example

Input:
10
1 2
1 3
2 4
1 5
1 6
4 7
7 8
5 9
1 10
10
0 6
0 6
0 6
1 3
0 1
0 1
1 3
1 10
1 4
1 6

Output:
2
2
2
3
0