Problem Statement

You are given $N integers A_1, A_2, \dots, A_N$.
Find the number of triples of integers (i, j, k) that satisfy the following conditions:

• $1 \le i, j, k \le N$
• $A_i \times A_j = A_k$

Input

The input is given from Standard Input in the following format:
N
A_1
A_2
$\vdots$
A_N

Output

Print the answer as an integer.

Constraints

• $1 \le N \le 1000$
• $\color{red}{1 \le A_i < 10^{1000}}$

Sample Input 1

5
2
3
6
12
24

Sample Output 1

6

The following six triples (i, j, k) satisfy the conditions in the problem statement:

• (1, 2, 3)
• (1, 3, 4)
• (1, 4, 5)
• (2, 1, 3)
• (3, 1, 4)
• (4, 1, 5)

Sample Input 2

11
1
2
3
4
5
6
123456789123456789
123456789123456789
987654321987654321
987654321987654321
121932631356500531347203169112635269

Sample Output 2

40

Note that the values of each integer A_i can be huge.

Sample Input 3

9
4
4
4
2
2
2
1
1
1

Sample Output 3

162

Note that there may be duplicates among the values of A_i.

见题面 Input 部分

见题面 Output 部分