We propose a novel transition-based algorithm that straightforwardly parses sentences from left to right by building $n$n attachments, with $n$n being the length of the input sentence. Similarly to the recent stack-pointer parser by Ma et al. (2018), we use the pointer network framework that, given a word, can directly point to a position from the sentence. However, our left-to-right approach is simpler than the original top-down stack-pointer parser (not requiring a stack) and reduces transition sequence length in half, from 2$n$n-1 actions to $n$n. This results in a quadratic non-projective parser that runs twice as fast as the original while achieving the best accuracy to date on the English PTB dataset (96.04% UAS, 94.43% LAS) among fully-supervised single-model dependency parsers, and improves over the former top-down transition system in the majority of languages tested.