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Default Counting characters within a cell

In order to help update an existing spreadsheet, I want to be able to count
either the number of numbers in a given cells, or alternatively the number
off addition signs.

i.e.
A1 =125+65+122+35

In A2 I'd like to be able to count either the number of numbers(eg. 4
numbers in this example where 125 is a single number), or the number of +'s
(and then add one) so that I can calculate the delivery fees based on the
number of deliveries (which is what the cell represents)

Changing the spreadsheet to hold all the data in seperate cells while being
easier from this point of view is not an option.

Thanks
 
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