ggplot2 - how to create a clustered timeline?

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How would you go about creating the graph below in R? I want to show the duration of different treatments for different patients.

Clustered Timeline

Mock data here:

                       Start Day    Stop Day
Patient 1   Drug 1     1            3
            Drug 2     2            5
            Drug 3     3            8
Patient 2   Drug 1     2            4
            Drug 2     2            5
            Drug 3     1            6
Patient 3   Drug 1     4            7
            Drug 2     3            8
            Drug 3     5            6
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