Sarah is planning her monthly budget. She needs to allocate her income of $3,000 among the following categories: rent, groceries, utilities, and savings. She decides to spend half of her income on rent, 1/4 of the remaining income on groceries, 1/3 of what’s left after groceries on utilities, and the rest will go into her savings. How much money will Sarah allocate to each category? Let's think step by step and output the final answer within \boxed{}.
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