Given a tree with $n$ nodes, rooted at 1.

Perform $q$ queries. Each query provides a sequence, and you need to determine if it is a possible subsequence of a BFS order of the tree.

The definition of a BFS order here is: maintain a queue, initially containing the root. Each time an element $u$ is popped, push all of its children into the queue in some order.

The BFS order can be different for different queries; that is, the queries are independent.

Input

The first line contains a single positive integer $n$.

The second line contains $n - 1$ positive integers, representing the parents of nodes 2 through $n$. It is guaranteed that the parent of a node has a smaller index than the node itself.

The next line contains a single positive integer $q$, representing the number of queries.

The following $q$ lines each start with a positive integer $m$, representing the length of the query sequence, followed by $m$ positive integers representing the query sequence.

Note that the nodes in the query sequence may contain duplicates.

$1 \le n \le 3 \times 10^5$, $1 \le q, \sum m \le 5 \times 10^5$.

Output

Output $q$ lines, each containing either Yes or No, representing your answer.

Case-insensitive.

Examples

Input 1

6
1 1 3 2 4
10
4 3 6 2 5
1 4
3 2 4 5
5 2 5 4 6 3
3 1 4 2
3 5 6 3
5 4 5 2 6 1
4 4 3 2 5
4 4 6 2 3
3 3 2 6

Output 1

No
Yes
Yes
No
No
No
No
No
No
Yes