Score : $400$ points

Problem Statement

You are given an integer sequence $A = (A_1, \dots, A_N)$ of length $N$.

Find the number of triplets of integers $(i, j, k)$ satisfying all of the conditions below.

• $1 \leq i, j, k \leq N$
• $\frac{A_i}{A_j} = A_k$

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 2 \times 10^5 \, (1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $\ldots$ $A_N$

Output

Print the answer.

3
6 2 3

2

$(i, j, k) = (1, 2, 3), (1, 3, 2)$ satisfy the conditions.

1
2

0

10
1 3 2 4 6 8 2 2 3 7

62