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You are given a strictly increasing array of integers , and a positive integer . An **arithmetic triplet** with a gap of is defined as triplet of integers from where:

- Each value is unique, and the triplet is in increasing order:
- The difference in the values from and are both exactly the specified value

Return the **number of arithmetic triplets** with a gap of that exist in .

**Input:** nums = [1, 2, 4, 6, 7, 11, 12] ; diff = 5

**Output:** 2

**Explanation:** For a diff of 5, there are two valid triplets: (1,6,11) and (2,7,12)

Notice how we can rearrange the equations relating the triplet values to such that and are defined in terms of . In other words, for a given value of , we know exactly what and we need.

Therefore, we can iterate over each value in and just check if the corresponding values of and exist in . A set of all the values in will allow us to perform this check efficiently. Be sure to remember that sets and dictionaries in python are very efficient for lookups!