Large language models (LLMs) are revolutionizing how we interact with information, but they're not without their quirks. One persistent challenge is their struggle with long inputs, especially in tasks where the order of information *shouldn't* matter (like querying a database or analyzing a graph). It turns out, LLMs have 'blind spots' – they're more likely to 'remember' certain parts of the input than others. Researchers have discovered a clever trick: by strategically shuffling the input, we can dramatically boost LLM accuracy on these 'symmetric' tasks. Think of it like rearranging a deck of cards so the most important ones are at the top. This technique leverages a smaller 'helper' LLM to estimate which pieces of information are most crucial for answering the main query. Then, it reorders the input so these essential parts land in the LLM's 'sweet spots'. Experiments on various tasks, from graph analysis to database queries, show this reranking method can drastically improve accuracy, sometimes by as much as 99%! This research opens exciting new doors for maximizing the power of LLMs, paving the way for more reliable and efficient applications in data analysis and beyond. While the technique currently requires a smaller helper LLM and works best on tasks with varying levels of element relevance, it offers a valuable step toward harnessing the full potential of LLMs, even with their inherent limitations.