Count Unique (Long) Strings

Please try at C2

=N(MATCH(A2,A$2:A2,)=ROWS(A$2:A2))

your countif did not work b/c "floating point" issue in excell : Excel can not read big value, from 15 digits and upper

Values those exceed 15 digits, to compare to other one, need to be splitted into two part: 1st part is first 15 digits, 2nd part is the rest

If using countif, it should be countif(S) to count both condition 1st 15 and the rest ALL match together

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Another option is using: MATCH=ROW
any dupliacte value has its own row_index, but has same MATCH_index in specific range

For example, A2="abc", A3="abc"
1st "abc" has row_index is row(A2)=2, 2nd one is row(A3)=3
but both "abc" has match_index in range A2:A10 is 1

So to mark the 1st one and ignore the 2nd one, try MATCH(A2:A3,A2:A10)=ROW(A2:A10)
equals:
{2,2,..,.,..}={2,3,...,...}
in pairs, one by one:
{true,false,..,...,...,..}