Codeforces Round 523 (Div. 2) |
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Finished |

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data structures

dp

implementation

math

number theory

*1700

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C. Multiplicity

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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).

Input

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

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

Output

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

Examples

Input

2

1 2

Output

3

Input

5

2 2 1 22 14

Output

13

Note

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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