Why is the intersection of two quorums must be greater than N/3 when proving streamlet?

Why is the intersection of two quorums must be greater than N/3 when proving Streamlet, a blockchain consensus protocol [BY Chan, Elaine Shi, 2020]?

In Streamlet, honest node vote for proposed block in every round. When a block gain vote for more than 2N/3 distinct node, it's notarized. In this context, quorum is the set of distinct votes on a notarized block

Following statement confuses me: The quorum size have to be more than 2N/3 to ensure at most one block can be notarized in a round if the malicious node is less than N/3, because the intersection of two quorums must be greater than N/3 and only malicious block will equivocate. This intersection greater than N/3 seems come out of nowhere or do I miss something? why can't it be smaller? like N/5 or something else?

This statement and picture are from the material of streamlet in principles of blockchains (ECE 598PV) from illinois and also from the lecture (14:47) given by the author.

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