Understanding multiple table join with aggregation

I have a basic question on how JOIN works on multiple tables. I want to count occurrences of Foreign Key in link1 & link2

CREATE TABLE main (
   id SERIAL PRIMARY KEY,
   name text NOT NULL
);

CREATE TABLE link1 (
   id SERIAL PRIMARY KEY,
   main_id integer NOT NULL,
   CONSTRAINT main_id_fk FOREIGN KEY (main_id) REFERENCES main (id)
);

-- link2 is similar to link1

SQL Fiddle

Why does the query below give a product of counts (rather than sum) when the count is non-zero in both columns.

SELECT main.id, COUNT(link1.main_id) + COUNT(link2.main_id)
FROM main
LEFT JOIN link1 ON main.id=link1.main_id
LEFT JOIN link2 ON main.id=link2.main_id
GROUP BY main.id