Given a sequence, please design an algorithm that finds the longest decreasing subsequence. A subsequence ti is decreasing if for all i$,$ ti $>$ ti$+1.$ For example, if the input sequence is $2,3,5,4,1,5,3,4,5.$ The longest decreasing subsequence is $5,4,3$ or $5,4,1.$ The longest length is $3.$ Your algorithm only needs to give the longest length. $($Bonus$)$ If your algorithm can also output the subsequence $($if there are multiple optimal solutions, print any of them$),$ you can get some bonus points.