Regex to match if it contains same character 0 or 2 or 4 times next to each other

I need to create regex rule to match this kind of strings (the looking letter is 'a'):

• aa
• aaaa
• aabb
• aaaagg
• cccaazz
• dddaaaazz

but not:

• aaa
• aaaaa
• abb
• bbbaaa
• bbaazza

Tried with [a]{2}|[a]{4} but this wasn't working. Any idea?

/^[^a]*(?:aa){0,2}[^a]*$/

1. We need ^ and $ to match the whole string.
2. The [^a]* match any number of non-as. This makes sure only the middle part contains as.
3. (?:aa){0,2} matches zero aas (= empty), one aa (= aa) or two aas (= aaaa).

>>> ['aa', 'aaaa', 'aabb', 'aaaagg', 'cccaazz', 'dddaaaazz', 'aaa', 'aaaaa', 'abb', 'bbbaaa', 'bbaazza']
    .map(c => `${c}: ${/^[^a]*(?:aa){0,2}[^a]*$/.test(c)}`).join('\n')
"aa: true
aaaa: true
aabb: true
aaaagg: true
cccaazz: true
dddaaaazz: true
aaa: false
aaaaa: false
abb: false
bbbaaa: false
bbaazza: false"