Approach 1: Top-down
- Time:O(40 \cdot 2^n \cdot n), where n = |\texttt{hats}|
- Space:O(40 \cdot 2^n)
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Approach 2: Bottom-up 2D DP
- Time:O(40 \cdot 2^n \cdot n)
- Space:O(40 \cdot 2^n)
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Approach 3: Bottom-up 1D DP
- Time:O(40 \cdot 2^n \cdot n)
- Space:O(2^n)
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