A10875. Coprime Subsequences

Let's call a non-empty sequence of positive integers $a_{1},a_{2}...\ a_{k}$ coprime if the greatest common divisor of all elements of this sequence is equal to $1$ .

Given an array $a$ consisting of $n$ positive integers, find the number of its coprime subsequences. Since the answer may be very large, print it modulo $10^{9}+7$ .

Note that two subsequences are considered different if chosen indices are different. For example, in the array $[1,1]$ there are $3$ different subsequences: $[1]$ , $[1]$ and $[1,1]$ .

The first line contains one integer number $n$ ( $1<=n<=100000$ ).

The second line contains $n$ integer numbers $a_{1},a_{2}...\ a_{n}$ ( $1<=a_{i}<=100000$ ).

Print the number of coprime subsequences of $a$ modulo $10^{9}+7$ .

In the first example coprime subsequences are:

1. $1$
2. $1,2$
3. $1,3$
4. $1,2,3$
5. $2,3$

In the second example all subsequences are coprime.