HELP FINDING MANGA!!! Isekai

Please I have been looking for the past hour, does anyone know the name of the manga where (I don't know if all the information is correct but)
1) These two girls (classmates? friends?) transmigrated into a different world where they do have some previous knowledge about it so it's either from an otome game or book
2) One is engaged to the crown prince and the other the second prince and they vow to make sure they help each other out
3) The girl engaged to second prince bumps into crown prince while saving a cat and accidentally lands on him they talk and sparks fly
4) The crown prince fiancee and second prince meet and the fiancee tells him he shouldn't feel inferior and should be proud both princes are really sweet
5) Each of the above pairs start hanging out more and more and the girls always make sure to put in a good word about the other (I also remember them in the past life having complexes about looking different from their personalities which is different in the new life I think but I'm not sure)
6) At a party each of the princes annul their engagements and the girls are shocked because they thought things were going good but they find out later that the princes want to marry their girls they fell in love with

That's roughly what I remember of the plot but I loved reading that manga so please help if you can!
Thank you!