The Alternating Sum

The alternating sum of an array $A = [A_1, A_2, \ldots, A_N]$ is defined to be $$A_1 - A_2 + A_3 - \ldots + (-1)^{N-1}A_N$$ You are allowed to perform the following operation **at most once** on $A$: - Choose a subarray of $A$ of **odd** length, remove this subarray from the original array, and concatenate it at the end of the remaining array. In other words, pick $1\leq L \leq R \leq N$ such th