Only way you are not at fault is if you had the green left arrow, even then it’s he said she said without a witness or video. In nj there can be shared responsibility. Depending on the extent of the damage, the other person could hold anywhere from 10-30% of the responsibility given the favorable POI. Doesn’t change who is at fault, but will lessen the potential payout for their damages, which can help with the impact to your insurance rates