Understanding Linux CPU scheduling priority

Scheduling priority depends on scheduling class.
scheduling classes
- SCHED_FIFO: A First-In, First-Out real-time process
- SCHED_RR: A Round Robin real-time process
- SCHED_NORMAL: A conventional, time-shared process
Most  processes are SCHED_NORMAL
How to find out the scheduling class of a process.

# ps  command with “class” flag
#   TS  SCHED_OTHER (SCHED_NORMAL)
#   FF  SCHED_FIFO
#   RR  SCHED_RR
$  ps -e -o class,cmd | grep sshd
TS  /usr/sbin/sshd
#chrt command
$ chrt -p 1836
pid 1836's current scheduling policy: SCHED_OTHER
pid 1836's current scheduling priority: 0

Scheduling priorities
- Real-time process (SCHED_FIFO/SCHED_RR)  real-time priority , ranging from 1 (lowest priority) to 99 (higest priority).
- Conventional process  static priority(SCHED_NORMAL ),  ranging from 100 (highest priority) to 139 (lowest priority).
Nice value and static priority
Conventional process's  static priority = (120 + Nice value)
So user can use nice/renice command to  change nice value in order to change conventional process's priority.
By default, conventional process  starts with nice value of 0 which equals static priority 120
Checking  Real-time/Conventional process priority.
$ ps -e -o class,rtprio,pri,nice,cmd

CLS RTPRIO PRI  NI CMD
TS       -  21   0 init [3]
FF      99 139   - [watchdog/0]

Watchdog is a real time process (CLASS=SCHED_FIFO), whose real time priority is 99 (I think the PRI column  is irrelevant  for it)
init is  a conventional process (CLASS=SCHED_OTHER), whose nice is 0 and dynamic priority is 121 (100+21)(I think the RTPRIO column  is irrelevant for it  )
Why init's priority is 121 not 120? Please noted I used the term: dynamic priority not static priority.
dynamic priority = max (100, min (  static priority - bonus + 5, 139))
bonus is ranging from 0 to 10,  which is set by scheduler depends on the past history of the process; more precisely, it is related to the average sleep time of the process.
Changing  Real-time/Conventional process priority.
#Real-time process

$chrt 80  ps -e -o class,rtprio,pri,nice,cmd
..
FF      80 120   - ps -e -o class,rtprio,pri,nice,cmd
# Conventional  process
$nice -n 10  ps -e -o class,rtprio,pri,nice,cmd
...
TS       -  12  10 ps -e -o class,rtprio,pri,nice,cmd