Ian and Array Sorting

Description:

Input:

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

The first line of each test case consists of a single integer $$$n$$$ ($$$2\le n\le 3\cdot10^5$$$) — the number of elements in the array.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le 10^9$$$) — the elements of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3\cdot10^5$$$.

Output:

For each test case, output "YES" if there exists a sequence of operations which make the array non-decreasing, else output "NO".

You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).

Sample Input:

5
3
1 3 2
2
2 1
4
1 3 5 7
4
2 1 4 3
5
5 4 3 2 1

Sample Output:

YES
NO
YES
NO
YES

Note:

For the first test case, we can increase $$$a_2$$$ and $$$a_3$$$ both by $$$1$$$. The array is now $$$[1, 4, 3]$$$.

Then we can decrease $$$a_1$$$ and $$$a_2$$$ both by $$$1$$$. The array is now $$$[0, 3, 3]$$$, which is sorted in non-decreasing order. So the answer is "YES".

For the second test case, no matter how Ian perform the operations, $$$a_1$$$ will always be larger than $$$a_2$$$. So the answer is "NO" and Ian cannot pretend to be smart.

For the third test case, the array is already in non-decreasing order, so Ian does not need to do anything.