The alternating sum of a 0-indexed array is defined as the sum of the elements at even indices minus the sum of the elements at odd indices.

- For example, the alternating sum of `[4,2,5,3]` is `(4 + 5) - (2 + 3) = 4`.

Given an array `nums`, return the maximum alternating sum of any subsequence of `nums` (after reindexing the elements of the subsequence).

A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements' relative order. For example, `[2,7,4]` is a subsequence of `[4,2,3,7,2,1,4]` (the underlined elements), while `[2,4,2]` is not.

Example 1:

    Input: nums = [4,2,5,3]

    Output: 7

    Explanation: It is optimal to choose the subsequence [4,2,5] with alternating sum (4 + 5) - 2 = 7.

Example 2:

    Input: nums = [5,6,7,8]

    Output: 8

    Explanation: It is optimal to choose the subsequence [8] with alternating sum 8.

Example 3:

    Input: nums = [6,2,1,2,4,5]

    Output: 10

    Explanation: It is optimal to choose the subsequence [6,1,5] with alternating sum (6 + 5) - 1 = 10.

Constraints:

- `1 <= nums.length <= 105`
- `1 <= nums[i] <= 105`