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Default adding cells within an array

I'm trying to devise a way to add cells within an array following a set of
criteria.
I have an array with a series of zero and non-zero numbers. As an example:

1 0
2 0
3 1.2
4 1.3
5 1.4
6 0
7 1.1
8 1.8
9 0
10 0

I want to add all the numbers that are between the zeroes. That is, I would
like to have two separate values in the above example: one value that is the
sum of 1.2, 1.3, and 1.4 and a second value that equals the sum of 1.1+1.8.
I could manually go through the array and add each sum, but because there are
nearly 40 sums in each array and multiple arrays to do this calculation I
would like to find a function to perform this task for me. Any help would be
much appreciated.
 
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