Countif only if it exists for one particular criteria for only the first instance

Question

I am stuck with something that I feel like should be relatively simple.

I am trying to create a count column that only counts the IDs that are only classified with DC, and only counts it for the first instance.

Expected outcome:

So far what I thought of was to create an unique ID in order to only count the first instance:

I tried the following formula but it's not correct as it cannot correctly identify only the cells that fit my criteria.

=IF(A2=A1,0,COUNTIF($A$2:$A$7,C2:C7="DC"))

Any help is much appreciated.