Using day ranges with a single DayPickerInput

[PiotrRut]

Is it at all possible to have one DayPickerInput component, which only accepts one custom input from the component prop, and a custom styled picker via overlayComponent, and have it both set the correct range by picking two dates from the calendar picker dropdown, as well as getting the range from the single typed input.

In that case, if I type

10/01/2021 - 12/01/2020 

the dates range as well as the selected range on the overlay would populate with those days.

@gpbl