Discrete Math/Comp Sci.. clear explanation please. thanks in advance!

A permutation of length n is a rearrangement of the numbers {1, 2, ....., n}. A permutation is called a mountain permutation if the numbers reading from left to right first increase and then decrease. For example, the permutation 1 2 3 5 7 6 4 is a mountain permutation of length 7, and 2 5 4 3 1 is a mountain permutation of length 5. We also consider increasing permutations of the form 12 3 ...... n and decreasing permutations of the form n ........ 3 2 1 to be mountain permutations. For example, 1 2 3 4 and 4 3 21 are mountain permutations of length 4. (d) Describe how to encode a mountain permutation of length n using the number of bits you gave in part (c) (e) How would you encode 2 5 7 6 4 3 1? (f) Describe how to decode from a binary string to a mountain permutation of length n, if it has been encoded using the method you described in part (d) (g) How would you decode 1 0 0 0 0 1