An array $$$[b_1, b_2, \ldots, b_m]$$$ is a palindrome, if $$$b_i = b_{m+1-i}$$$ for each $$$i$$$ from $$$1$$$ to $$$m$$$. Empty array is also a palindrome.

An array is called kalindrome, if the following condition holds:

It's possible to select some integer $$$x$$$ and delete some of the elements of the array equal to $$$x$$$, so that the remaining array (after gluing together the remaining parts) is a palindrome.

Note that you don't have to delete all elements equal to $$$x$$$, and you don't have to delete at least one element equal to $$$x$$$.

For example :

$$$[1, 2, 1]$$$ is kalindrome because you can simply not delete a single element.
$$$[3, 1, 2, 3, 1]$$$ is kalindrome because you can choose $$$x = 3$$$ and delete both elements equal to $$$3$$$, obtaining array $$$[1, 2, 1]$$$, which is a palindrome.
$$$[1, 2, 3]$$$ is not kalindrome.

You are given an array $$$[a_1, a_2, \ldots, a_n]$$$. Determine if $$$a$$$ is kalindrome or not.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. 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 length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — elements of the array.

It's guaranteed that the sum of $$$n$$$ over all test cases won't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print YES if $$$a$$$ is kalindrome and NO otherwise. You can print each letter in any case.

Note

In the first test case, array $$$[1]$$$ is already a palindrome, so it's a kalindrome as well.

In the second test case, we can choose $$$x = 2$$$, delete the second element, and obtain array $$$[1]$$$, which is a palindrome.

In the third test case, it's impossible to obtain a palindrome.

In the fourth test case, you can choose $$$x = 4$$$ and delete the fifth element, obtaining $$$[1, 4, 4, 1]$$$. You also can choose $$$x = 1$$$, delete the first and the fourth elements, and obtain $$$[4, 4, 4]$$$.

Kalindrome Array

Examples