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In page Twelfth Amendment to the United States Constitution:

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Consequently, a contingent presidential election was held in the House of Representatives. Federalist-controlled state delegations cast their votes for Burr in an effort to prevent Jefferson from becoming president. Neither Burr nor Jefferson was able to win on the first 35 ballots. With help from Alexander Hamilton, the gridlock was finally broken on the 36th ballot and Jefferson was elected president on February 17, 1801.[3] This prolonged contingent election, combined with the increasing Democratic–Republican majorities in both the House and the Senate, set the stage for a constitutional amendment to alter this flawed system.[citation needed]