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Identifying and characterizing strings of NA in a vector

Dear R users,

I was wondering if someone could suggest a few lines of code for my problem.

I want to count the number and the length of strings of NA in a vector. 
For example:

vec <- c(1, 2, 1, NA, NA, 1, 2, NA, NA, NA, 3, 4, NA, NA)

has 2 strings of NA's of length 2 and 1 string of NA' of length 3.

I can easily count the number of NA's per vector, but I am having a hard 
time counting the number and length of strings of NA's per vector 
without relying heavily on loops. I will have to perform this task for 
many vectors.

Can somebody help?

many thanks,

Marie-Pierre