<p>A popular masseuse receives a sequence of back-to-back appointment requests and is debating which ones to accept. She needs a break between appointments and therefore she cannot accept any adjacent requests. Given a sequence of back-to-back appoint­ ment requests, find the optimal (highest total booked minutes) set the masseuse can honor. Return the number of minutes.</p> <p><b>Note: </b>This problem is slightly different from the original one in the book.</p> <p> </p> <p><strong>Example 1: </strong></p> <pre> <strong>Input: </strong> [1,2,3,1] <strong>Output: </strong> 4 <strong>Explanation: </strong> Accept request 1 and 3, total minutes = 1 + 3 = 4 </pre> <p><strong>Example 2: </strong></p> <pre> <strong>Input: </strong> [2,7,9,3,1] <strong>Output: </strong> 12 <strong>Explanation: </strong> Accept request 1, 3 and 5, total minutes = 2 + 9 + 1 = 12 </pre> <p><strong>Example 3: </strong></p> <pre> <strong>Input: </strong> [2,1,4,5,3,1,1,3] <strong>Output: </strong> 12 <strong>Explanation: </strong> Accept request 1, 3, 5 and 8, total minutes = 2 + 4 + 3 + 3 = 12 </pre>