(1) Determine the amount of statues Inspired by this stack of little statues that are currently on my desk at work, given to me by my colleagues from Sri Lanka when they visited The Netherlands:

This is split into two different challenges due to popular demand:
Part 1) Determine the amount of statues (this challenge)
Part 2) Can the statues be stacked?
Challenge 1:
Input:
\$statues\$: a multi-line string (or character matrix), containing only the characters  \n|-# (where the  |-# can be other characters of your own choice)
Output:
The amount of statues in the input.
Statues input example:
      ##|
####    |
# ##
#  #  |##
----  |######
      |   ###
|##   |##   #
|## - |######
    # |####

The | and - represent the bases of the statues. So with the input above, we'll have the following statues:
       ####
       ## #
       ## ##
####   #  ##
# ##  ## ###  ##      #
#  #  ## ###  ##  #   #
----  ------  --  -  --

So the output will be 5.
Challenge rules:

You can use a different consistent character other than #, -, and/or | for the statue if you want ( \n are mandatory, though). Please state which one you've used in your answer if it's different than the defaults.
You are allowed to take the \$statues\$ input in any reasonable format. Can be a multi-line string, a list/array/stream of strings, a character matrix, etc.
You are allowed to pad the statues input with trailing spaces so it's a rectangle.
You can assume statues are always separated by at least one space or blank line from one-another, so something like #|#| or #||# won't be in the input.
You can assume the statues will only have a base at ones side, so a statue like this won't be in the input:


##|
##|
--


It is possible that a smaller statue is within the rectangular boundaries of another oddly shaped statue. For example, this is possible:


# ##
- ##
  ##
####
# # 
----


Statues will never be inside of each other, though. So something like this won't be in the input:


 #####
##   #
#  # #
# ## ##
# -- ##
#     #
##    #
-------


You can assume the base determines the width of a statue. So you won't have statues like these in the input:


#######
 #####
 ####     ###
  ---     --

General rules:

This is code-golf, so shortest answer in bytes wins.
Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language.
Standard rules apply for your answer with default I/O rules, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs. Your call.
Default Loopholes are forbidden.
If possible, please add a link with a test for your code (i.e. TIO).
Also, adding an explanation for your answer is highly recommended.

Test cases:
      ##|
####    |
# ##
#  #  |##
----  |######
      |   ###
|##   |##   #
|## - |######
    # |####

Output: 5
__________________________________________________

# ##
- ##
  ##
####
# # 
----

Output: 2
__________________________________________________

      #
|###  #
| #   #
|#### -

Output: 2
__________________________________________________

--- ##|
### ##|
###
### |#

Output: 3
__________________________________________________

####             #####|
# ##
###              |#           |#
#####            |#           |##
-----            |#           |#
                 |#
                 |#
                 |#

Output: 4
__________________________________________________

|# |# |# |# |# #| #| #|

Output: 8
__________________________________________________

|##
|   ##
|#  --

Output: 2
__________________________________________________

      |##
----  |####
# ##
###   |#
      |#  ###|
      |#    #|
      |#   ##|
      |#

Output: 4
__________________________________________________

- |##
#      #
  #| ###
  #| ---

Output: 4
__________________________________________________

#
####
----

--
 #

Output: 2
__________________________________________________
##
##
--

--
##
##

Output: 2
05AB1E, 15 bytes
„-|v€Åγ˜y¢Iø}Š+

Try it online!
Commented:
„-|              # push string literal &quot;-|&quot;
   v        }    # iterate over this string
    €Åγ          #   run-length encode each line of the input / transposed input
                 #   this pushes the chunk elements and the chunk lengths
       ˜         #   flatten the list
        y¢       #   count the chunks of the current character
          Iø     #   push the transposed input to the stack for the second iteration
             Š   # triple-swap: move the transposed input to bottom
              +  # sum both counts