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Greybox fuzzing is the de-facto standard to discover bugs during development. Fuzzers execute many inputs to maximize the amount of reached code. Recently, Directed Greybox Fuzzers (DGFs) propose an alternative strategy that goes beyond "just" coverage: driving testing toward specific code targets by selecting "closer" seeds. DGFs go through different phases: exploration (i.e., reaching interesting locations) and exploitation (i.e., triggering bugs). In practice, DGFs leverage coverage to directly measure exploration, while exploitation is, at best, measured indirectly by alternating between different targets. Specifically, we observe two limitations in existing DGFs: (i) they lack precision in their distance metric, i.e., averaging multiple paths and targets into a single score (to decide which seeds to prioritize), and (ii) they assign energy to seeds in a round-robin fashion without adjusting the priority of the targets (exhaustively explored targets should be dropped). We propose FishFuzz, which draws inspiration from trawl fishing: first casting a wide net, scraping for high coverage, then slowly pulling it in to maximize the harvest. The core of our fuzzer is a novel seed selection strategy that builds on two concepts: (i) a novel multi-distance metric whose precision is independent of the number of targets, and (ii) a dynamic target ranking to automatically discard exhausted targets. This strategy allows FishFuzz to seamlessly scale to tens of thousands of targets and dynamically alternate between exploration and exploitation phases. We evaluate FishFuzz by leveraging all sanitizer labels as targets. Extensively comparing FishFuzz against modern DGFs and coverage-guided fuzzers shows that FishFuzz reached higher coverage compared to the direct competitors, reproduces existing bugs (70.2% faster), and finally discovers 25 new bugs (18 CVEs) in 44 programs.