You are given a 0indexed integer array books
of length n
where books[i]
denotes the number of books on the i^{th}
shelf of a bookshelf.
You are going to take books from a contiguous section of the bookshelf spanning from l
to r
where 0 <= l <= r < n
. For each index i
in the range l <= i < r
, you must take strictly fewer books from shelf i
than shelf i + 1
.
Return the maximum number of books you can take from the bookshelf.
Example 1:
Input: books = [8,5,2,7,9]
Output: 19
Explanation:
 Take 1 book from shelf 1.
 Take 2 books from shelf 2.
 Take 7 books from shelf 3.
 Take 9 books from shelf 4.
You have taken 19 books, so return 19.
It can be proven that 19 is the maximum number of books you can take.
Example 2:
Input: books = [7,0,3,4,5]
Output: 12
Explanation:
 Take 3 books from shelf 2.
 Take 4 books from shelf 3.
 Take 5 books from shelf 4.
You have taken 12 books so return 12.
It can be proven that 12 is the maximum number of books you can take.
Example 3:
Input: books = [8,2,3,7,3,4,0,1,4,3]
Output: 13
Explanation:
 Take 1 book from shelf 0.
 Take 2 books from shelf 1.
 Take 3 books from shelf 2.
 Take 7 books from shelf 3.
You have taken 13 books so return 13.
It can be proven that 13 is the maximum number of books you can take.
Constraints:
1 <= books.length <= 10^{5}
0 <= books[i] <= 10^{5}

