Count number of instances where a blank exists in one of 2 columns + r

Question

I need to test a dataframe for completion of records - for the records to be complete an entry must be made in both columns. In in the example df below you will see that 2 of the 9 entries contain blanks in one of the rows.

df <- data.frame(a = c(1,2,"",4,5,6,7,"",8,9),
                 b = c(9,5,2,7,5,"",3,"",6,8))

The desired output would be a count of 2 or 7 identifying the number of records that are complete or conversely incomplete. Instances where both are blanks would not be considered in the count.