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.

**Example**

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

**Function Description**

Complete the *beautifulTriplets* function in the editor below.

beautifulTriplets has the following parameters:

*int d:*the value to match*int arr[n]:*the sequence, sorted ascending

**Returns**

*int:*the number of beautiful triplets

**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**

**Sample Input**

STDIN Function ----- -------- 7 3 arr[] size n = 7, d = 3 1 2 4 5 7 8 10 arr = [1, 2, 4, 5, 7, 8, 10]

**Sample Output**

```
3
```

**Explanation**

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 .