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 $N$, $A$, find the number of subarrays $[L,R]$ $1\le L\le R\le N$ such that $B\le max(A_{[L,R]})-min(A_{[L,R]})\le T$.

Note: $max(A_{[L,R]})$ denotes the maximum value in the range $[L,R]$ in $A$; likewise, $min(A_{[L,R]})$ denotes the minimum value in the range $[L,R]$ in $A$.

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

Can you help him?

Constraints

$-{10}^9\le A_i\le {10}^9$

$0\le B\le T\le 2\times {10}^9$

Subtask 1 [20%]

$1\le N\le 2000$

Subtask 2 [80%]

$1\le N\le 1000000$

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

Input Specification

The first line will contain $N$, $B$, and $T$, 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 $N$ 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 $[B,T]$.

Sample Input

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

Sample Output

6

Explanation for Sample Output

There are $6$ distinct subarrays that have a difference of exactly $3$: $[1,2],[2,4],[2,5],[3,4],[3,5],[6,8]$.