The alternating sum of an array indexed from $0$ is defined as the sum of the elements at even indices minus the sum of the elements at odd indices.

For instance, the alternating sum of an array $[a_0, a_1, a_2, a_3]$ equals $(a_0 + a_2) - (a_1 + a_3)$.

Given an integer array nums, return the maximum possible alternating sum of any subsequence of nums after indexing the chosen subsequence starting from $0$.

A subsequence of an array is a sequence obtained by deleting some (possibly zero) elements from the original array without altering the relative order of the remaining elements.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

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