Drew Brees had the most games with 3+ passing touchdowns, 300+ passing yards and exactly 0 intercepted passes, with 39 games.

who has the most games with 300 passing yards, 3 passing touchdowns, and 0 interceptions
Interpreted as:
Who has the most regular-season games with 300 or more passing yards, 3 or more passing touchdowns, and 0 passing interceptions?

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