Count distinct from a bootstrapped sample

Question

I have a dataset of N items, with attribute V which can be repetitive, for example:

City | Country
--------------
NYC  | USA
LA   | USA
LON  | UK
MAN  | UK
AMS  | NL

After bootstrapping the dataset into M groups on size N with replacement, I want to estimate the COUNT(DISTINCT V) in each of the group. However since the bootstrapping is with replacement, some of the element might repeat, and the cardinality of V will be smaller then the original.

For example I could get in one of the groups:

City | Country
--------------
NYC  | USA
LA   | USA
LON  | UK
LON  | UK
NYC  | USA

and then the estimation of COUNT(DISTINCT Country) would be 2 instead of 3.

Is there a way to estimate the original value through the values from bootstrapping?