J. Triple Reverse Sort

You are given a permutation $a$ of length $n$.

On this permutation, we can perform the following operation multiple times:

1. Select an index $i$ such that $1 \le i \le n-2$;
2. Reverse the subarray $[a_i,a_{i+1},a_{i+2}]$.

Is it possible to sort the permutation?

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 testcases. The first line of each testcase contains an integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of each testcase contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of permutation $a$.

The second line of each testcase contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$, all $a_i$ are pairwise distinct) — the elements of permutation $a$.

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

Output

For each testcase, print YES if $a$ can be sorted, or NO otherwise.

Example

stdin

6
1
1
2
2 1
3
3 2 1
4
4 3 2 1
5
1 3 2 5 4
5
3 4 5 2 1

stdout

YES
NO
YES
NO
NO
YES

Note

In the first two testcases, no operations can be performed since $n \lt 3$. $[1]$ is already sorted, while $[2,1]$ is not.

In the third testcase, the permutation can be sorted by choosing $i=1$ and reversing $[a_1,a_2,a_3]$.

In the fourth and fifth testcases, it can be proven that $a$ cannot be sorted.