CF1061C.Multiplicity

You are given an integer array $a_1, a_2, \ldots, a_n$.

The array $b$ is called to be a subsequence of $a$ if it is possible to remove some elements from $a$ to get $b$.

Array $b_1, b_2, \ldots, b_k$ is called to be good if it is not empty and for every $i$ ($1 \le i \le k$) $b_i$ is divisible by $i$.

Find the number of good subsequences in $a$ modulo $10^9 + 7$.

Two subsequences are considered different if index sets of numbers included in them are different. That is, the values of the elements do not matter in the comparison of subsequences. In particular, the array $a$ has exactly $2^n - 1$ different subsequences (excluding an empty subsequence).

给你一个整数数组 $a_1, a_2, \ldots, a_n$。

若可通过从 $a$ 中删除若干元素得到数组 $b$，则称 $b$ 是 $a$ 的一个子序列。

若数组 $b_1, b_2, \ldots, b_k$ 非空，且对每个 $i$（$1 \le i \le k$）均有 $b_i$ 被 $i$ 整除，则称其为“好”的子序列。

求 $a$ 中“好”子序列的个数，结果对 $10^9 + 7$ 取模。

当两个子序列所包含元素的下标集合不同时，认为它们是不同的子序列。换言之，在比较子序列时，元素的值无关紧要。特别地，数组 $a$ 恰有 $2^n - 1$ 个不同的子序列（不包括空子序列）。

The first line contains an integer $n$ ($1 \le n \le 100\,000$) — the length of the array $a$.

The next line contains integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^6$).

第一行包含一个整数 $n$（$1 \le n \le 100\,000$）—— 数组 $a$ 的长度。

第二行包含整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^6$）。

Print exactly one integer — the number of good subsequences taken modulo $10^9 + 7$.

输出一个整数——即“好”子序列的数量对 $10^9 + 7$ 取模的结果。

In the first example, all three non-empty possible subsequences are good: ${1}$, ${1, 2}$, ${2}$

In the second example, the possible good subsequences are: ${2}$, ${2, 2}$, ${2, 22}$, ${2, 14}$, ${2}$, ${2, 22}$, ${2, 14}$, ${1}$, ${1, 22}$, ${1, 14}$, ${22}$, ${22, 14}$, ${14}$.

Note, that some subsequences are listed more than once, since they occur in the original array multiple times.

在第一个例子中，所有三个非空的可能子序列都是好的：${1}$、${1, 2}$、${2}$。

在第二个例子中，可能的好子序列有：${2}$、${2, 2}$、${2, 22}$、${2, 14}$、${2}$、${2, 22}$、${2, 14}$、${1}$、${1, 22}$、${1, 14}$、${22}$、${22, 14}$、${14}$。

注意，某些子序列被多次列出，因为它们在原数组中多次出现。