A15512 | Challenging Valleys

You are given an array $a[0 \dots n-1]$ of $n$ integers. This array is called a "valley" if there exists exactly one subarray $a[l \dots r]$ such that:

- $0 \le l \le r \le n-1$ ,
- $a_l = a_{l+1} = a_{l+2} = \dots = a_r$ ,
- $l = 0$ or $a_{l-1} > a_{l}$ ,
- $r = n-1$ or $a_r < a_{r+1}$ .

Here are three examples:

The first image shows the array \[ $3, 2, 2, 1, 2, 2, 3$ \], it is a valley because only subarray with indices $l=r=3$ satisfies the condition.

The second image shows the array \[ $1, 1, 1, 2, 3, 3, 4, 5, 6, 6, 6$ \], it is a valley because only subarray with indices $l=0, r=2$ satisfies the codition.

The third image shows the array \[ $1, 2, 3, 4, 3, 2, 1$ \], it is not a valley because two subarrays $l=r=0$ and $l=r=6$ that satisfy the condition.

You are asked whether the given array is a valley or not.

Note that we consider the array to be indexed from $0$ .

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

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 2\cdot10^5$ ) — the length of the array.

The second line of each test case contains $n$ integers $a_i$ ( $1 \leq a_i \leq 10^9$ ) — the elements of the array.

It is guaranteed that the sum of $n$ over all test cases is smaller than $2\cdot10^5$ .

For each test case, output "YES" (without quotes) if the array is a valley, and "NO" (without quotes) otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).