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.

Note: This problem is slightly different from the original one in the book.

Example 1:

Input:  [1,2,3,1]

Output:  4

Explanation:  Accept request 1 and 3, total minutes = 1 + 3 = 4

Example 2:

Input:  [2,7,9,3,1]

Output:  12

Explanation:  Accept request 1, 3 and 5, total minutes = 2 + 9 + 1 = 12

Example 3:

Input:  [2,1,4,5,3,1,1,3]

Output:  12

Explanation:  Accept request 1, 3, 5 and 8, total minutes = 2 + 4 + 3 + 3 = 12