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 2\,000~

Subtask 2 [80%]

~1 \le N \le 1\,000\,000~

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]~.