给定一个包含 $n$ 个正整数的数组 $a$，求满足以下分数不可约的互不相同的下标四元组 $(i, j, k, l)$ 的数量，即满足 $\gcd(a_i \cdot a_j, a_k \cdot a_l) = 1$ 的四元组数量：
$$\frac{a_i \cdot a_j}{a_k \cdot a_l}$$
第一行包含一个整数 $n$ ($4 \le n \le 2000$)，表示数组的长度。第二行包含 $n$ 个整数 $a_i$ ($1 \le a_i \le 10^{12}$)，表示数组的元素。
输出一个整数：满足给定条件的四元组数量。
4 1 1 1 1
24
6 10 11 2 4 5 7
96
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