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E - Prefix Equality

Score : $500$ points

Problem Statement

You are given integer sequences $A = (a_1,\ldots,a_N)$ and $B = (b_1,\ldots,b_N)$, each of length $N$.

For $i=1,...,Q$, answer the query in the following format.

• If the set of values contained in the first $x_i$ terms of $A$, $(a_1,\ldots,a_{x_i})$, and the set of values contained in the first $y_i$ terms of $B$, $(b_1,\ldots,b_{y_i})$, are equal, then print Yes; otherwise, print No.

Constraints

• $1 \leq N,Q \leq 2 \times 10^5$
• $1 \leq a_i,b_i \leq 10^9$
• $1 \leq x_i,y_i \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $\ldots$ $a_N$

$b_1$ $\ldots$ $b_N$

$Q$

$x_1$ $y_1$

$\vdots$

$x_Q$ $y_Q$

Output

Print $Q$ lines. The $i$-th line should contain the response to the $i$-th query.

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

Yes
Yes
Yes
No
No
Yes
No

Note that sets are a concept where it matters only whether each value is contained or not.
For the $3$-rd query, the first $2$ terms of $A$ contain one $1$ and one $2$, while the first $3$ terms of $B$ contain one $1$ and two $2$'s. However, the sets of values contained in the segments are both $\{ 1,2 \}$, which are equal.
Also, for the $6$-th query, the values appear in different orders, but they are still equal as sets.