Mongolian National Mathematical Olympiad

$n$ girls are standing in a circle, each holding exactly 1 card. One girl gives her card to the girl on her left, who in turn gives 2 cards to the girl on her left. The girl who got the cards gives 1 card to the girl on her left. The girl who got the card gives 2 cards to the girl on her left. Continuing this way, each girl gives alternating 1 or 2 cards to the girl on her left. Anyone who has no card leaves the game immediately. Find all values of $n$ such that all cards are collected by one girl.