Problem Description

Given a set $a$ of size $n$, all elements are guaranteed to be distinct and are all positive integers.

If we pick three elements $a, b, c$ from it in order, then there are $n \cdot (n-1) \cdot (n-2)$ different ways to choose.

Now for one choice $(a,b,c)$, define its weight as $\Bigl\lfloor\dfrac{a}{b}\Bigr\rfloor\Bigl\lfloor\dfrac{a}{c}\Bigr\rfloor\Bigl\lfloor\dfrac{b}{c}\Bigr\rfloor$.

You need to compute the sum of weights over all choices. You only need to output this sum modulo $2^{32}$.

Note: $\lfloor a\rfloor$ denotes the greatest integer not greater than $a$. For example, $\lfloor 2.4\rfloor=2$ and $\lfloor 5\rfloor=5$.

Input Format

The first line contains a positive integer $n$, the length of the sequence.

The second line contains $n$ positive integers $a_1, a_2, \ldots, a_n$. Each number describes one element of the set $a$, and all these numbers are distinct.

Output Format

Output one line with one integer, the answer modulo $2^{32}$.

4
1 2 3 4

36

6
8 6 4 2 10 15

268

Hint

[Sample Explanation #1]

For sample #1, the only choices with non-zero weight are:

• $(3,2,1)$, with weight $6$.
• $(4,2,1)$, with weight $16$.
• $(4,3,1)$, with weight $12$.
• $(4,3,2)$, with weight $2$.

Therefore, the answer for sample #1 is $6+16+12+2=36$.

[Constraints]

For $100\%$ of the testdata, $1 \le n, a_i \le 5000$.

This problem uses bundled tests.

Special Property A: it is guaranteed that $a_i=i$.

[Hint]

In this problem, most algorithms have small constant factors. Please trust your time complexity.

Translated by ChatGPT 5