(Python) Check whether a password contains at least two uppercase letters and two lowercase letters by using recording in variable 'requirements'

I wonder: The requirement should be 2, but its outcome is 6. How can Isolve the problem?

password = 'PAssword1$'
def is_password_valid(password):
requirements = 0

upper_case = []
for j in password:
    if j.isupper():
        upper_case.append(j)
        if len(upper_case) > 1:
            requirements += 1

lower_case = []
for j in password:
    if j.islower():
        lower_case.append(j)
        if len(lower_case) > 1:
            requirements += 1

print(requirements)

is_password_valid(password)