We call a sequence of integers a$1,...,$ an noisy when the signs of the differences between two con$-$

secutive terms in the sequence strictly alternate between $+$ and $($the difference is never zero$).$

So the sequence either follows a$1<$ a$2>$ a$3<$ a$4>...$ or it follows a$1>$ a$2<$ a$3>$ a$4<...$ You are

given an array of integers A $=[$a$1,...,$ an$].$

Design a dynamic programming algorithm to find the length of the longest noisy subsequence in

A$.$

Example:

Input: A $=[2,4,1,5,9,7,9,0,5,5,2]$

Output: $7$

Explanation: An example of a noisy subsequence from the above array A is $2,4,1,9,0,5,2.$

There are more examples, but the length is the same for all. On the other hand, $2,4,7,9,0,5,5$

is not a noisy subsequence because the differences between the three consecutive elements $2,4,$

and $7$ do not alternate. Two $5$s also show up at the end of the sequence causing the consecutive

difference to be zero