Problem Statement

You are given a connected simple undirected graph G with N vertices numbered 1 to N and N edges. The i-th edge connects Vertex u_i and Vertex v_i bidirectionally.
Answer the following Q queries.

• Determine whether there is a unique simple path from Vertex x_i to Vertex y_i (a simple path is a path without repetition of vertices).

Input

Input is given from Standard Input in the following format:
N
u_1 v_1
u_2 v_2
$\vdots$
u_N v_N
Q
x_1 y_1
x_2 y_2
$\vdots$
x_Q y_Q

Output

Print Q lines.
The $i-th line (1 \leq i \leq Q)$ should contain Yes if there is a unique simple path from Vertex x_i to Vertex y_i, and No otherwise.

Constraints

• $3 \leq N \leq 2 \times 10^5$
• $1 \leq u_i < v_i\leq N$
• $(u_i,v_i) \neq (u_j,v_j)$ if $i \neq j$.
• G is a connected simple undirected graph with N vertices and N edges.
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq x_i < y_i\leq N$
• All values in input are integers.

Sample Input 1

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

Sample Output 1

No
Yes
No

The simple paths from Vertex 1 to 2 are (1,2) and (1,3,2), which are not unique, so the answer to the first query is No.
The simple path from Vertex 1 to 4 is (1,4), which is unique, so the answer to the second query is Yes.
The simple paths from Vertex 1 to 5 are (1,2,5) and (1,3,2,5), which are not unique, so the answer to the third query is No.

Sample Input 2

10
3 5
5 7
4 8
2 9
1 2
7 9
1 6
4 10
2 5
2 10
10
1 8
6 9
8 10
6 8
3 10
3 9
1 10
5 8
1 10
7 8

Sample Output 2

Yes
No
Yes
Yes
No
No
Yes
No
Yes
No

见题面 Input 部分

见题面 Output 部分