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- Beautiful Triplets

# Beautiful Triplets

# Beautiful Triplets

Given a sequence of integers , a triplet is beautiful if:

Given an increasing sequenc of integers and the value of , count the number of beautiful triplets in the sequence.

For example, the sequence and . There are three beautiful triplets, by index: . To test the first triplet, and .

**Function Description**

Complete the *beautifulTriplets* function in the editor below. It must return an integer that represents the number of beautiful triplets in the sequence.

beautifulTriplets has the following parameters:

*d*: an integer*arr*: an array of integers, sorted ascending

**Input Format**

The first line contains space-separated integers and , the length of the sequence and the beautiful difference.

The second line contains space-separated integers .

**Constraints**

**Output Format**

Print a single line denoting the number of beautiful triplets in the sequence.

**Sample Input**

```
7 3
1 2 4 5 7 8 10
```

**Sample Output**

```
3
```

**Explanation**

The input sequence is , and our beautiful difference . There are many possible triplets , but our only beautiful triplets are , and by value not index. Please see the equations below:

Recall that a beautiful triplet satisfies the following equivalence relation: where .