Score: $550$ points

问题描述

你已知 $N$ 个整数 $A_1, A_2, \dots, A_N$。
找出满足以下条件的整数三元组 $(i, j, k)$ 的数量：

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

以上为通义千问 qwen-max 翻译，仅供参考。

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:

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

Constraints

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

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.

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 $A_i$.

update @ 2024/3/10 01:31:46