Write a Python program to check the validity of password input by users:
Passwords MUST contain the following:
At least 1 letter between [a-z] and 1 letter between [A-Z].
At least 1 number between [0-9].
At least 1 character from [$#@].
Minimum length 6 characters.
Maximum length 16 characters.
Also, each of the above checks should be written as a function