A-B-C Sort

2000ms

262144K

Description:

You are given three arrays $$$a$$$, $$$b$$$ and $$$c$$$. Initially, array $$$a$$$ consists of $$$n$$$ elements, arrays $$$b$$$ and $$$c$$$ are empty.

You are performing the following algorithm that consists of two steps:

Step $$$1$$$: while $$$a$$$ is not empty, you take the last element from $$$a$$$ and move it in the middle of array $$$b$$$. If $$$b$$$ currently has odd length, you can choose: place the element from $$$a$$$ to the left or to the right of the middle element of $$$b$$$. As a result, $$$a$$$ becomes empty and $$$b$$$ consists of $$$n$$$ elements.
Step $$$2$$$: while $$$b$$$ is not empty, you take the middle element from $$$b$$$ and move it to the end of array $$$c$$$. If $$$b$$$ currently has even length, you can choose which of two middle elements to take. As a result, $$$b$$$ becomes empty and $$$c$$$ now consists of $$$n$$$ elements.

Refer to the Note section for examples.

Can you make array $$$c$$$ sorted in non-decreasing order?

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. Next $$$t$$$ cases follow.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^6$$$) — the array $$$a$$$ itself.

It's guaranteed that the sum of $$$n$$$ doesn't exceed $$$2 \cdot 10^5$$$.

For each test, print YES (case-insensitive), if you can make array $$$c$$$ sorted in non-decreasing order. Otherwise, print NO (case-insensitive).

YES
NO
YES

In the first test case, we can do the following for $$$a = [3, 1, 5, 3]$$$:

Step $$$1$$$:

$$$a$$$	$$$[3, 1, 5, 3]$$$	$$$\Rightarrow$$$	$$$[3, 1, 5]$$$	$$$\Rightarrow$$$	$$$[3, 1]$$$	$$$\Rightarrow$$$	$$$[3]$$$	$$$\Rightarrow$$$	$$$[]$$$
$$$b$$$	$$$[]$$$		$$$[\underline{3}]$$$		$$$[3, \underline{5}]$$$		$$$[3, \underline{1}, 5]$$$		$$$[3, \underline{3}, 1, 5]$$$

Step $$$2$$$:

$$$b$$$	$$$[3, 3, \underline{1}, 5]$$$	$$$\Rightarrow$$$	$$$[3, \underline{3}, 5]$$$	$$$\Rightarrow$$$	$$$[\underline{3}, 5]$$$	$$$\Rightarrow$$$	$$$[\underline{5}]$$$	$$$\Rightarrow$$$	$$$[]$$$
$$$c$$$	$$$[]$$$		$$$[1]$$$		$$$[1, 3]$$$		$$$[1, 3, 3]$$$		$$$[1, 3, 3, 5]$$$

As a result, array $$$c = [1, 3, 3, 5]$$$ and it's sorted.

Informação

Provedor Codeforces

Código CF1674D