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<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&shy; ment requests, find the optimal (highest total booked minutes) set the masseuse can honor. Return the number of minutes.</p>
<p><b>Note:&nbsp;</b>This problem is slightly different from the original one in the book.</p>
<p>&nbsp;</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>