SQL: count number of distinct values in every column

I need a query that will return a table where each column is the count of distinct values in the columns of another table.

I know how to count the distinct values in one column:

select count(distinct columnA) from table1;

I suppose that I could just make this a really long select clause:

select count(distinct columnA), count(distinct columnB), ... from table1;

but that isn't very elegant and it's hardcoded. I'd prefer something more flexible.