This is the hard version of the problem. The only differences between the two versions of this problem are the constraints on $$$n$$$ and the time limit. You can make hacks only if all versions of the problem are solved.

You are given two arrays $$$a$$$ and $$$b$$$ of length $$$n$$$.

You can perform the following operation some (possibly zero) times:

choose $$$l$$$ and $$$r$$$ such that $$$1 \leq l \leq r \leq n$$$.
let $$$x=\max(a_l,a_{l+1},\ldots,a_r)$$$.
for all $$$l \leq i \leq r$$$, set $$$a_i := x$$$.

Determine if you can make array $$$a$$$ equal to array $$$b$$$.

Input

Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of the arrays.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the elements of array $$$a$$$.

The third line contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le n$$$) — the elements of array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output "YES" (without quotes) if you can make $$$a$$$ into $$$b$$$ using any number of operations, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).

Note

In the first test case, we can achieve array $$$b$$$ by applying a single operation: $$$(l,r)=(2,3)$$$.

In the second test case, it can be shown we cannot achieve array $$$b$$$ in any amount of operations.

In the third test case, we can achieve array $$$b$$$ by applying two operations: $$$(l,r)=(2,5)$$$. followed by $$$(l,r)=(1,3)$$$.

In the fourth and fifth test cases, it can be shown we cannot achieve array $$$b$$$ in any amount of operations.

Set To Max (Hard Version)

Examples