How did the presidential election of 1800 lead to establishment of the twelfth amendment?

Hamilton told the federalists that they should put blank votes so Jefferson could have more of them.

Because of this,

The Twelfth Amendment was passed in 1804, and it importantly altered the U. S. Electoral College to allow electors to vote for both a President and a Vice-President in a presidential election, instead of voting for two different presidential candidates, or the same presidential candidate twice.