This Python program solves the classic ancient Chinese puzzle involving chickens and rabbits on a farm, given the total number of heads and legs. The program uses a system of linear equations to efficiently compute the number of chickens and rabbits based on the provided input. The solution checks for edge cases, such as impossible combinations, and returns the appropriate number of chickens and rabbits or indicates when no solution exists. The algorithm is optimized to run in constant time (O(1)).
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