SQL to find sum of total days in a window for a series of changes

Following is the table:

start_date recorded_date id
2021-11-10 2021-11-01 1a
2021-11-08 2021-11-02 1a
2021-11-11 2021-11-03 1a
2021-11-10 2021-11-04 1a
2021-11-10 2021-11-05 1a

I need a query to find the total day changes in aggregate for a given id. In this case, it changed from 10th Nov to 8th Nov so 2 days, then again from 8th to 11th Nov so 3 days and again from 11th to 10th for a day, and finally from 10th to 10th, that is 0 days.

In total there is a change of 2+3+1+0 = 6 days for the id – ‘1a’.

Basically for each change there is a recorded_date, so we arrange that in ascending order and then calculate the aggregate change of days grouped by id. The final result should be like:

id Agg_Change
1a 6

Is there a way to do this using SQL. I am using vertica database.