Need a formula to extract name of fathers and place them in the same rows with mothers

So I have ~130k rows with names of kids, mostly 2 rows per kid (about 65k kids) with same info in each 2 rows however one has the father's name and the other mother's name. I want to have only one row per kid with one colum with mother's name and other column with father's name. However not all rows are in the same order father-mother sequence, some of them hare mother-father and other are single mom or single dad.

I have been traying several ifs/ands formulas but cannot discriminate either the order nor if is a single mom as the sequence of rows (in pairs) which do not apply when finding a kid with single mom/dad.

Driving me nuts. Hope someone can help.

Many thanks in advance.

P.S. Excuse my English as its a 2nd tounge.

=IF(AND(E2=E3,G2="DAD",G3="Mom"),H2,H3).
names.png

I'm sure someone else will come with better formula...

I don't want to use Index or match, just personal preference

at cell I2

Formula:

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at cell J2

Formula:

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drag down to fill the formula

Thank you Biex, I will try this after dinner time. I really appreciate your effort mate. I will let you know. Regards.

if you wish using your own formula on column I...

you may use only this formula on J2

Formula:

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drag down to fill formula

Thanks again Biex, I did try your second formula above but didn't work (the one to be used on J2). Your first post formula looks promising. Only thing is that for some reason excel gets very slow in resolving, I have not tried yet with 130K records.
I will get back tomorrow with the outcome. Again thanks for your support. Blessings.

Biex,
Your formula did the trick. I wanted to appreciate your help.
You a are such a great person.
Hope I can help someone else just like you did.
Many many thanks again, blessing for you and yours.
Cheers mate.

The formula could be improve and optimize further more... If God will, I will try to optimize it....

You are most welcome...