Given an array of integers nums, determine the maximum alternating subarray sum among all non empty subarrays of nums.

The alternating sum of a subarray starting at index i and ending at index j inclusive ($i \leq j$) is evaluated as:

nums[i] $-$ nums[i + 1] $+$ nums[i + 2] $-$ nums[i + 3] $+ \dots$

where the signs alternate between addition and subtraction, beginning with addition for the first element nums[i].

Return the maximum alternating sum of any non empty subarray.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $-10^5 \leq$ nums[i] $\leq 10^5$

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