Hard Sequence

Chef decided to write an infinite sequence. Initially, he wrote $0$, and then he started repeating the following process: - Look at the last element written so far (the $l$-th element if the sequence has length $l$ so far); let's denote it by $x$. - If $x$ does not occur anywhere earlier in the sequence, the next element in the sequence is $0$. - Otherwise, look at the previous occurrence of $x