You are given a permutation $a$ of length $n$$^{\text{∗}}$.

You can perform the following operation any number of times (possibly zero):

• Select an index $i$ ($1 \le i \le \frac{n}{2}$), and swap $a_i$ and $a_{2i}$.

For example, when $a=[1,4,2,3,5]$, you can swap $a_2$ and $a_4$ to make it $[1,3,2,4,5]$, but you cannot swap $a_2$ and $a_3$.

Please determine if the sequence $a$ can be sorted in increasing order.

$^{\text{∗}}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). 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 second line of each test case contains $n$ distinct integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$).

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

Output

If $a$ can be sorted in increasing order, output "YES" on a separate line. Otherwise, output "NO" on a separate line.

You can output the answer in any case. For example, the strings "yEs", "yes", and "Yes" will also be recognized as positive responses.

Note

In the first test case, $a$ is $[1,4,3,2,5]$. You can sort $a$ in increasing order by swapping $a_2$ and $a_4$. Therefore, the answer is "YES".

In the second test case, $a$ is $[1,4,2,3,5]$. It is impossible to sort $a$ in increasing order. Therefore, the answer is "NO".

Samples

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

YES
NO