Scheme RSR5

All problems are to be solved using R5RS within drracket, no vectors, no strings, no assignment ... Question: ; For this problem, we will think of 0 as a convenient substitute for a left bracket, ; and 1 as a convenient substitute for a right bracket. ; A sequence of 0s and 1s is said to be balanced if (i) every 0 is later ; closed by some 1, and (ii) every 1 closes a previous 0. ; Thus ((0 1)) is the list of all balanced sequences of length 2, and ; ( (0 0 1 1) (0 1 0 1) ) is a list of all balanced sequences of ; length 4 ; Assuming n is a positive even integer, write and prove correct ; a function bal so that (bal n) returns a list - without duplicates - ; of all balanced sequences of 0s and 1s of length n. Your program ; should be as efficient as you can reasonably make it: at the very least, it should not generate ; any unbalanced sequences in the course of computing the final result. ; (hint: you will need a carefully considered recursive design and several ; auxiliary functions; I suggest that you use structural induction)