D. A-B-C Sort
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

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).

Example
Input
343 1 5 333 2 117331
Output
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 $2$:

 $b$ $[3, 3, \underline{1}, 5]$ $\Rightarrow$ $[3, \underline{3}, 5]$ $\Rightarrow$ $[\underline{3}, 5]$ $\Rightarrow$ $[\underline{5}]$ $\Rightarrow$ $[]$ $c$ $[]$ $[1]$ $[1, 3]$ $[1, 3, 3]$ $[1, 3, 3, 5]$
As a result, array $c = [1, 3, 3, 5]$ and it's sorted.