Problem Statement

A Kadomatsu sequence is a sequence $A_1, A_2, A_3$ consisting of $3$ elements that satisfies the following 2 conditions.

• $A_1, A_2, A_3$ are all distinct
• Among the $3$ elements, $A_2$ is the largest or $A_2$ is the smallest

For a graph in which vertex $i$ has value $Ai$, a cycle is called a Kadomatsu cycle if it satisfies the following 2 conditions.

• The cycle has 3 or more vertices
• Letting $u,v,w$ denote 3 consecutive vertices on the cycle, for all $u,v,w$, the sequence $A_u,A_v,A_w$ is a Kadomatsu sequence

There is a tree with $N$ vertices in which vertex $i$ has value $Ai$.
Adding a new edge connecting vertex $u$ and vertex $v$ ($u \neq v$) to this tree creates exactly one cycle.
Is the cycle created in this way a Kadomatsu cycle? Answer this for each of the $Q$ edges.
Print "YES" if it is a Kadomatsu cycle and "NO" otherwise, one per line.

Input

$N$
$A_1$ $A_2$ $\dots$ $A_N$
$x_1$ $y_1$
$x_2$ $y_2$
$\vdots$
$x_{N-1}$ $y_{N-1}$
$Q$
$u_1$ $v_1$
$u_2$ $v_2$
$\vdots$
$u_Q$ $v_Q$

The 1st line gives the number of vertices $N$ of the tree.
The 2nd line gives the values $A_i$ of the vertices $i$, separated by spaces.
The following $N-1$ lines, starting from the 3rd line, give the edges. The $i$-th edge connects vertex $x_i$ and vertex $y_i$.
Line 3+N-1 gives the number $Q$ of edges to be newly added.
The following $Q$ lines, starting from line 3+N, give the edges to be newly added. The $i$-th edge connects vertex $u_i$ and vertex $v_i$.
Each of the $Q$ edges is added to the tree independently. The edge added $i$-th does not affect the graph for the $j$-th edge ($i \neq j$).

All input values are integers and satisfy the following constraints.
$2 \leq N \leq 10^5$
$1 \leq A_i \leq 10^5$
$1 \leq x_i,y_i \leq N$
$x_i \neq y_i$
The tree is guaranteed to be connected and to have no multiple edges or self-loops.

$1 \leq Q \leq 10^5$
$1 \leq u_i, v_i \leq N$
$u_i \neq v_i$

Since the amount of input and output is large, using the fastest possible I/O is recommended. Of the 4-second execution time limit, 2 seconds are intended to be for I/O.

Output

For each edge, print on one line "YES" if the cycle created by adding the new edge to the tree is a Kadomatsu cycle, and "NO" otherwise.

Sample

7
1 5 4 6 3 4 3
1 2
2 3
3 4
2 5
1 6
6 7
4
4 5
4 7
5 7
3 5

YES
YES
NO
NO

7
1 5 4 6 3 4 3
1 2
2 3
3 4
4 5
5 6
6 7
5
1 2
1 5
3 7
6 1
1 4

NO
NO
NO
YES
YES