Counting Issue In Table

I have a table with the following data (sample)

Type Year Price
---- ---- -----
A 00 100.00
A 00 200.00
A 01 105.00
A 01 105.00-
B 00 100.00
B 00 200.00
B 01 105.00
B 02 00.00


I need to establish a Type Count. The business rule to do the count is -

For a particular type, take a single year and add up the price. If the price is greater than zero then count = 1 else count = 0. After completing the counts for all the years for a particular type, add up the counts.

Based on the business rule for the above sample data I should have the following count.

Count -
Type A = 1 (For Year 00, price = 300.00 so count = 1 and for year 01, price = .00 (105 + 105.00 - ) and so count = 0. add counts to get a total of 1)

Type B = 2 (For Year 00, price = 300.00 so count = 1 and for year 01, price = 105 and so count = 1 and for year 02 price = 00 so count = 0. add counts to get a total of 2)

How do I implement this count using a query. I am free to add any indicator columns that may be required to perform the counting.

Let me know.

Thanks

Vivek