Xiao Z, a lover of Japanese cuisine, frequently visits the conveyor belt sushi restaurant outside the school's east gate. Here, plates of sushi are presented to Xiao Z one by one on a conveyor belt. Different sushi provide different taste experiences for Xiao Z. We define a satisfaction value for each plate of sushi; for example, Xiao Z loves salmon, so his satisfaction for a plate of salmon sushi is 10; Xiao Z finds tuna to be bland, so his satisfaction for a plate of tuna sushi is only 5; Xiao Z recently watched the movie "The Mermaid" and was disgusted by the octopus in it, so his satisfaction for a plate of octopus sashimi is -100.

In particular, Xiao Z is a famous foodie, and he has a habit when eating conveyor belt sushi that we call "eating non-stop." Specifically, after he eats a plate of sushi from the conveyor belt, he will eat the subsequent sushi without hesitation until he no longer wants to eat any more. Today, Xiao Z has come to this conveyor belt sushi restaurant again. $N$ plates of sushi will pass in front of him in sequence, where his satisfaction with the $i$-th plate of sushi is $A_i$. Xiao Z can choose which plate to start eating from and which plate to stop at. He wants to know how many different choices exist such that the sum of his satisfaction is no less than $L$ and no greater than $R$.

Note that although this is conveyor belt sushi, we do not consider this a problem on a ring, but rather a problem on a line. That is, what Xiao Z can eat is a contiguous subsequence of the input sequence; after the last plate passes by, the first plate will not appear again.

Input

The first line contains three integers $N$, $L$, and $R$, representing the number of sushi plates, the lower bound of satisfaction, and the upper bound of satisfaction, respectively.

The second line contains $N$ integers $A_i$, representing Xiao Z's satisfaction with the sushi.

Output

A single line containing an integer, representing the total number of choices such that the sum of Xiao Z's satisfaction is no less than $L$ and no greater than $R$.

Examples

Input 1

5 5 9
1 2 3 4 5

Output 1

6

Subtasks

For $10\%$ of the data, $N \leq 100$.

For $20\%$ of the data, $N \leq 1\,000$.

Another $10\%$ of the data, $A_i \geq 0$, $L = 0$.

Another $20\%$ of the data, $A_i \geq 0$.

Another $20\%$ of the data, $|A_i| \leq 100$.

For $100\%$ of the data, $N \le 100\,000$, $|A_i| \le 100\,000$, $0 \le L, R \le 10^9$.