1815A · Ian and Array Sorting

Problem: To thank Ian, Mary gifted an array $a$ of length $n$ to Ian. To make himself look smart, he wants to make the array in non-decreasing order by doing the following finitely many times: he chooses two adjacent elements $a_i$ and $a_{i+1}$ ($1\le i\le n-1$), and increases both of them by $1$ or decreases both of them by $1$. Note that, the elements of the array can become negative.

As a smart person, you notice that, there are some arrays such that Ian cannot make it become non-decreasing order! Therefore, you decide to write a program to determine if it is possible to make the array in non-decreasing order.

Input Format: 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 Format: 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).

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.