count (DISTINCT field) OVER ()

I would like to implement the equivalent of "count (DISTINCT field) OVER
()":


SELECT
  id, name, similarity(name, 'Tooneyvara') as delta,
  count (id) OVER() AS cnt
  FROM vtown
  WHERE
      similarity(name, 'Tooneyvara') > 0.1
  ORDER BY  delta DESC

produces result:
1787    Toomyvara    0.5    4
1787    Toomevara    0.4    4
1700    Ardcroney    0.105    4
1788    Townsfield    0.1    4

What I would like is a "3" in the cnt column (ignoring id duplicates).


How can I achieve this?


The best I can come up with is:

SELECT id, name,delta,  count (*) OVER()
FROM (
SELECT DISTINCT ON (id)
  id, name, similarity(name, 'Tooneyvara') as delta
  FROM vtown
  WHERE
    similarity(name, 'Tooneyvara') > 0.1
    ORDER BY id, delta DESC
) AS x
ORDER by delta DESC

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Best Regards,
Tarlika Elisabeth Schmitz