Write and test a function reformat$\_$date that takes three strings: a date string, an input date format, and an output date format. This function should return a new date string formatted according to the output date format.

A date string is a non$-$empty string of numbers separated by $/,$ such as $"2/20/1991"$ or $"1991/02/20".$ The order of date fields $($month$,$ day, year$)$ will depend on the date format, and the number of digits for each field can vary but there must be at least one digit for each field.

A date format is a non$-$empty string of the date symbols $"$D$","$M$","$Y$"$ separated by $/.$ Assume the date string will match the date formats $($share the same number of $/$s$),$ that any date symbol in the output date format will also appear in the input date format, and that date formats do not duplicate date symbols.