There are two brothers name Hazel (Bob) and Laurel (James). Their mom told them to buy $n$ products from the store. There is one condition according to which they can shop:

Bob can bring the items that have the price difference greater than or equal to $X$ with each other and James can bring the items that have the price difference greater than or equal to $Y$ with each other. 

You are required to determine the number of ways in which both of them can bring the items home.

Note: As the number of ways can be greater, print the answer modulo $1e9+7$.

Input format

• The first line contains three integers $n$, $X$, and $Y$ denoting the number of items, the price difference for Bob, and the price difference for James respectively.
• The second line contains $n$ integers where $A_i$ denotes the prices of the products.

Output format

Print the number of ways modulo 1e9+7.

Constraints

$1 \le N \le 1e5\\ 1 \le X,\ Y \le 1e18\\ 0 \le A_i \le 1e18$