Given $n$ positive integers $a_i$, find the number of pairs $(i, j)$ such that $1 \le i \le n$, $1 \le j \le n$, $i \neq j$, and $a_i$ is a multiple of $a_j$.

Input

The first line contains an integer $n$, representing the number of integers. The second line contains $n$ integers representing $a_i$.

Output

Output a single integer representing the answer.

Examples

Input 1

6
16 11 6 1 9 11

Output 1

7

Constraints

For 40% of the data: $n \le 1000$. For 70% of the data: $1 \le a_i \le 5 \times 10^3$. For 100% of the data: $2 \le n \le 2 \times 10^5$, $1 \le a_i \le 5 \times 10^5$.