Given a tree graph with N vertices and Q queries.
The i-th query consists of mi special vertices x1,x2,x3,…xmi.
A vertex u on the tree is considered to be occupied by a special vertex x if the distance from u to x is the smallest among the mi special vertices (if the distance from u to x1 is equal to the distance from u to x2 and x1<x2, then u will preferentially be occupied by x1).
For each query, print the number of vertices that each special vertex xi occupies.
### Input
- The first line contains an integer N.
- The next N−1 lines describe the edges of the tree.
- The following line contains an integer Q.
- The next Q×2 lines are structured as follows:
- The first line contains an integer mi.
- The next line contains mi integers x1,x2,…, which are the special vertices.
### Output
- Output the answer for each query in the order of the input.
### Constraints
- N,Q≤500000.
- mi,xi≤n.
- ∑Qi=1mi ≤500000
### Example
Input:
1021324354617383941011487103
Output:
1135