Description

Given an array $a$ whose length is $n$ and two integers $k_1$ and $k_2$. In one operation, you can choose an index $i$ ($1\le i\le n$) and add either $k_1$ or $k_2$ to $a_i$.

For an unordered integer pair $(i,j)$ ($1\le i,j\le n, i\neq j$), if you can perform a finite number of times (which can be zero) of the operation, resulting in $a_i=a_j$, then the pair $(i,j)$ is good.

Count the number of good unordered pairs in the array.

Input

The first line contains three integers $n,k_1,k_2$ ($2\le n\le 10^5,1\le k_1,k_2\le 10^6$).

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le 10^6$), indicating the array.

Output

Output an integer indicating the answer.

Samples

6 56482 114514
6 6 6 6 6 6

15

3 7 2
11 21 7

3

6 1 1
58 45 15 25 26 9

15

Note

For the second example, all pairs meet the requirements. For example, with the pair $(1, 2)$, choosing $i$ as 1 and adding $k_2$, after performing this operation five times, we have $a_1 = 21$ and $a_2 = 21$; thus, the pair $(1, 2)$ satisfies the requirement. Please note that $(1, 2)$ and $(2, 1)$ are considered the same pair.

Resources

电子科技大学第十五届 ACM 趣味程序设计竞赛