CF1016G.Appropriate Team

Since next season are coming, you'd like to form a team from two or three participants. There are $n$ candidates, the $i$-th candidate has rank $a_i$. But you have weird requirements for your teammates: if you have rank $v$ and have chosen the $i$-th and $j$-th candidate, then $GCD(v, a_i) = X$ and $LCM(v, a_j) = Y$ must be met.

You are very experienced, so you can change your rank to any non-negative integer but $X$ and $Y$ are tied with your birthdate, so they are fixed.

Now you want to know, how many are there pairs $(i, j)$ such that there exists an integer $v$ meeting the following constraints: $GCD(v, a_i) = X$ and $LCM(v, a_j) = Y$. It's possible that $i = j$ and you form a team of two.

$GCD$ is the greatest common divisor of two number, $LCM$ — the least common multiple.

由于新赛季即将到来，你希望从两名或三名参与者中组建一支队伍。现有 $n$ 名候选人，其中第 $i$ 名候选人的排名为 $a_i$。但你对队友有特殊要求：若你的排名为 $v$，且你选中了第 $i$ 名和第 $j$ 名候选人，则必须满足 $GCD(v, a_i) = X$ 且 $LCM(v, a_j) = Y$。

你经验非常丰富，因此可将自身排名调整为任意非负整数；但 $X$ 和 $Y$ 与你的生日绑定，故其值固定不变。

现在你想知道：有多少对 $(i, j)$ 满足——存在某个整数 $v$，使得约束条件 $GCD(v, a_i) = X$ 与 $LCM(v, a_j) = Y$ 同时成立？注意 $i = j$ 是允许的，此时你将组建一支两人队伍。

其中 $GCD$ 表示两个数的最大公约数，$LCM$ 表示两个数的最小公倍数。

First line contains three integers $n$, $X$ and $Y$ ($1 \le n \le 2 \cdot 10^5$, $1 \le X \le Y \le 10^{18}$) — the number of candidates and corresponding constants.

Second line contains $n$ space separated integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^{18}$) — ranks of candidates.

第一行包含三个整数 $n$、$X$ 和 $Y$（$1 \le n \le 2 \cdot 10^5$，$1 \le X \le Y \le 10^{18}$）——分别为候选人数量及对应的常数。

第二行包含 $n$ 个用空格分隔的整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^{18}$）——表示各位候选人的排名。

Print the only integer — the number of pairs $(i, j)$ such that there exists an integer $v$ meeting the following constraints: $GCD(v, a_i) = X$ and $LCM(v, a_j) = Y$. It's possible that $i = j$.

输出唯一的整数——满足如下条件的数对 $(i, j)$ 的个数：存在整数 $v$，使得 $GCD(v, a_i) = X$ 且 $LCM(v, a_j) = Y$。允许 $i = j$。

In the first example next pairs are valid: $a_j = 1$ and $a_i = [2, 4, 6, 8, 10, 12]$ or $a_j = 2$ and $a_i = [2, 4, 6, 8, 10, 12]$. The $v$ in both cases can be equal to $2$.

In the second example next pairs are valid:

• $a_j = 1$ and $a_i = [1, 5, 7, 11]$;
• $a_j = 2$ and $a_i = [1, 5, 7, 11, 10, 8, 4, 2]$;
• $a_j = 3$ and $a_i = [1, 3, 5, 7, 9, 11]$;
• $a_j = 6$ and $a_i = [1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2]$.

在第一个例子中，以下数对是合法的：$a_j = 1$ 且 $a_i = [2, 4, 6, 8, 10, 12]$，或 $a_j = 2$ 且 $a_i = [2, 4, 6, 8, 10, 12]$。在这两种情况下，$v$ 均可取值为 $2$。

在第二个例子中，以下数对是合法的：

• $a_j = 1$ 且 $a_i = [1, 5, 7, 11]$；
• $a_j = 2$ 且 $a_i = [1, 5, 7, 11, 10, 8, 4, 2]$；
• $a_j = 3$ 且 $a_i = [1, 3, 5, 7, 9, 11]$；
• $a_j = 6$ 且 $a_i = [1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2]$。