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for the lowest and highest values you can use only 2 occurrence of each and for the values between these you can only use max. 3 of each distinct ones. Tension: Generating a solution is another problem because you may have plenty of solutions for the same input. Outcome: So the max is 8. | I need to form a new list having size n with the below features. Tension: The new list must satisfy the above properties, and it need not have all the elements from the original input list. Outcome: return the value 7. | The greatest length of the solution seems be the size of the problem minus the number of values that can't be used. Tension: you may have plenty of solutions for the same input. Outcome: for [1,1,1,2,2,2,2,3,3,3] you are losing 1 "1", 1 "3" and you can only use 3 of the 4 "2", so max is 7.