You are given a sequence of $n$ integers $a_1, a_2, \ldots, a_n$. You should determine the number of such ordered pairs $(i, j)$, that $i, j \in \{1, \ldots, n\}$, $i \ne j$ and $a_i$ is a divisor of $a_j$.

Input

The first line of input contains one integer $n$ ($1 \le n \le 2\,000\,000$). The second line contains a sequence of $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 2\,000\,000$).

Output

In the first and only line of output should contain one integer, denoting the number of pairs sought.

Examples

Input 1

5
2 4 5 2 6

Output 1

6

Note

There are 6 pars with the specified properties: $(1, 2)$, $(1, 4)$, $(1, 5)$, $(4, 1)$, $(4, 2)$, $(4, 5)$.