Match Intersection with exact number of related nodes

WITH ["Ram", "Sita", "Hari"] as names
MATCH (u:User)-[:IS_PARTICIPANT]->(c:Conversation)
WHERE u.name IN names
WITH c, size(names) as inputCnt, count(DISTINCT u) as userCnt
WHERE userCnt = inputCnt and size(()-[:IS_PARTICIPANT]->(c)) = inputCnt
RETURN c