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.

Input

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

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

Output

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.

Examples

Input

12 2 2
1 2 3 4 5 6 7 8 9 10 11 12


Output

12


Input

12 1 6
1 3 5 7 9 11 12 10 8 6 4 2


Output

30

Note

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].

Source: codeforces | Difficulty: VERY_HARD
Tags: Number theory

Bit manipulation

Mathematics


Solutions: