| Mocha likes arrays, so before her departure, Bazoka gave her an array $a$ consisting of $n$ positive integers as a gift. | |
| Now Mocha wants to know whether array $a$ could become sorted in non- decreasing order after performing the following operation some (possibly, zero) times: | |
| * Split the array into two parts — a prefix and a suffix, then swap these two parts. In other words, let $a=x+y$. Then, we can set $a:= y+x$. Here $+$ denotes the array concatenation operation. | |
| For example, if $a=[3,1,4,1,5]$, we can choose $x=[3,1]$ and $y=[4,1,5]$, satisfying $a=x+y$. Then, we can set $a:= y + x = [4,1,5,3,1]$. We can also choose $x=[3,1,4,1,5]$ and $y=[\,]$, satisfying $a=x+y$. Then, we can set $a := y+x = [3,1,4,1,5]$. Note that we are not allowed to choose $x=[3,1,1]$ and $y=[4,5]$, neither are we allowed to choose $x=[1,3]$ and $y=[5,1,4]$, as both these choices do not satisfy $a=x+y$. | |
| Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 1000$). The description of the test cases follows. | |
| The first line of each test case contains a single integer $n$ ($2\leq n\leq 50$) — the length of the array $a$. | |
| The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^6$) — the elements of array $a$. | |
| For each test case, output "Yes" if $a$ could become non-decreasing after performing the operation any number of times, and output "No" if not. | |
| You can output "Yes" and "No" in any case (for example, strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive response). | |
| In the first test case, it can be proven that $a$ cannot become non- decreasing after performing the operation any number of times. | |
| In the second test case, we can perform the following operations to make $a$ sorted in non-decreasing order: | |
| * Split the array into two parts: $x=[7]$ and $y=[9,2,2,3]$, then swap these two parts. The array will become $y+x = [9,2,2,3,7]$. * Split the array into two parts: $x=[9]$ and $y=[2,2,3,7]$, then swap the |