Given a list of integers and a target integer, return the number of triplets whose product is the target integer and two adjacent triplets



Question: Given a list of integers (possibly negative) and a target integer, return the number of triplets whose product is the target integer and two of the triplets must be adjacent.

More precisely, given a triplet $ (i,j,k)$ with $ i<j<k,$ it satisfies the question above if $ A[i] \times A[j] \times A[k] = target$ and either ($ j = i+1$ and $ k > j+1$ ) or ($ k = j+1$ and $ i < j -1$ .)

For example, if the list given is $ A = [1,2,2,2,4]$ and target $ = 8,$ then the answer is $ 3$ as $ (0, 1, 4) , (1, 2, 3)$ and $ (0, 3, 4)$ are the only triplets satisfying conditions above if we use $ 0$ -based numbering.

I stucked at this question for 3 hours and not able to solve it.

Any hint is appreciated.