<p>The <strong>alternating sum</strong> of a <strong>0-indexed</strong> array is defined as the <strong>sum</strong> of the elements at <strong>even</strong> indices <strong>minus</strong> the <strong>sum</strong> of the elements at <strong>odd</strong> indices.</p> <ul> <li>For example, the alternating sum of <code>[4,2,5,3]</code> is <code>(4 + 5) - (2 + 3) = 4</code>.</li> </ul> <p>Given an array <code>nums</code>, return <em>the <strong>maximum alternating sum</strong> of any subsequence of </em><code>nums</code><em> (after <strong>reindexing</strong> the elements of the subsequence)</em>.</p> <ul> </ul> <p>A <strong>subsequence</strong> 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, <code>[2,7,4]</code> is a subsequence of <code>[4,<u>2</u>,3,<u>7</u>,2,1,<u>4</u>]</code> (the underlined elements), while <code>[2,4,2]</code> is not.</p> <p> </p> <p><strong>Example 1:</strong></p> <pre> <strong>Input:</strong> nums = [<u>4</u>,<u>2</u>,<u>5</u>,3] <strong>Output:</strong> 7 <strong>Explanation:</strong> It is optimal to choose the subsequence [4,2,5] with alternating sum (4 + 5) - 2 = 7. </pre> <p><strong>Example 2:</strong></p> <pre> <strong>Input:</strong> nums = [5,6,7,<u>8</u>] <strong>Output:</strong> 8 <strong>Explanation:</strong> It is optimal to choose the subsequence [8] with alternating sum 8. </pre> <p><strong>Example 3:</strong></p> <pre> <strong>Input:</strong> nums = [<u>6</u>,2,<u>1</u>,2,4,<u>5</u>] <strong>Output:</strong> 10 <strong>Explanation:</strong> It is optimal to choose the subsequence [6,1,5] with alternating sum (6 + 5) - 1 = 10. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= nums.length <= 10<sup>5</sup></code></li> <li><code>1 <= nums[i] <= 10<sup>5</sup></code></li> </ul>