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  1. Correctness: The solutions are correct and cover different approaches, including brute-force and optimized methods. Well done!
  2. Time Complexity: The second and third methods are more efficient than the reference solution, which is excellent.
  3. Space Complexity: The third method reduces space usage effectively, which is a significant improvement over the reference solution.
  4. Code Quality: The code is clean, readable, and well-commented. The use of meaningful variable names and clear logic is commendable.
  5. Efficiency: The student has already considered optimizations, so no further suggestions are needed here.

One minor suggestion: In the third method, the variable name ans could be more descriptive, such as result or output, to maintain consistency with the other methods.

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