Count number of events between two dynamic timestamps in pandas dataframe

Question

I want to create a dataframe showing the number of total events within changing time intervals. In other words, I want to find the number of datapoints with time that fall between certain timestamps.

First, my dataframe looks like below:

| id  | time              | first_time        | thirty_min_bf_first_time
| --  | ----------------- |--- --- --- --- -- |--- --- --- --- --- --- 
| 121 | 22/01/01 00:02:00 | 22/01/01 00:32:00 | 22/01/01 00:02:00
| 121 | 22/01/01 01:22:34 | 22/01/01 00:32:00 | 22/01/01 00:02:00
| 245 | 22/04/01 12:00:00 | 22/04/01 12:00:00 | 22/04/01 11:30:00
| 245 | 22/04/01 13:23:34 | 22/04/01 12:00:00 | 22/04/01 11:30:00

I created 'first_time' and 'thirty_min_bf_first_time' columns based on 'time' for each events. what I want to create is a dataframe like below:

| id  | total_events_btw_times |
| --  | -- ------------------- |
| 121 | 12                     |
| 245 | 34                     |

The new dataframe should be grouped by id and have a column showing total events between each time interval between df['thirty-min_bf_first_time'] and df['first_time'].

I have tried many things but didn't work out. Can anyone please help me out? Thanks!