After setting all his ideas for bugaboos, Max has decided to blindly steal from others he saw online.

Recently, he read an interesting bugaboo on a new online judge called JOMD:

Given an array of length , , find the number of subarrays such that .

**Note: denotes the maximum value in the range in ; likewise, denotes the minimum value in the range in .**

This bugaboo stumped Max, so he asked you for help.

Can you help him?

#### Constraints

##### Subtask 1 [20%]

##### Subtask 2 [80%]

**Note: Fast I/O might be required to fully solve this problem (e.g., BufferedReader for Java).**

#### Input Specification

The first line will contain , , and , the number of elements in the array and the minimum and maximum difference between the maximum and minimum in the subarrays.

The next line will contain space-separated integers, the elements of the array.

#### Output Specification

Output the number of distinct subarrays that have a difference between the maximum and minimum in .

#### Sample Input

```
8 3 3
1 4 5 2 2 -3 -5 -6
```

#### Sample Output

`6`

#### Explanation for Sample Output

There are distinct subarrays that have a difference of exactly : .

## Comments