A-B-C Sort
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.
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).
Input
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 $2 \cdot 10^5$.
Output
For each test, print YES (case-insensitive), if you can make array $c$ sorted in non-decreasing order. Otherwise, print NO (case-insensitive).
Samples
3
4
3 1 5 3
3
3 2 1
1
7331
YES
NO
YES
Note
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 $2$:
| $b$ | $[3, 3, \underline{1}, 5]$ | $\Rightarrow$ | $[3, \underline{3}, 5]$ | $\Rightarrow$ | $[\underline{3}, 5]$ | $\Rightarrow$ | $[\underline{5}]$ | $\Rightarrow$ | $[]$ |
| $c$ | $[]$ | $[1]$ | $[1, 3]$ | $[1, 3, 3]$ | $[1, 3, 3, 5]$ |