CF1815A Ian and Array Sorting

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.

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 $ .

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).

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.