Coprime Subsequences

2000ms

262144K

Description:

Let's call a non-empty sequence of positive integers a₁, a₂... 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 10⁹ + 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].

Input:

The first line contains one integer number n (1 ≤ n ≤ 100000).

The second line contains n integer numbers a₁, a₂... a_n (1 ≤ a_i ≤ 100000).

Output:

Print the number of coprime subsequences of a modulo 10⁹ + 7.

Sample Input:

3
1 2 3

Sample Output:

Sample Input:

4
1 1 1 1

Sample Output:

Sample Input:

7
1 3 5 15 3 105 35

Sample Output:

Note:

In the first example coprime subsequences are:

1
1, 2
1, 3
1, 2, 3
2, 3

In the second example all subsequences are coprime.

Informação

Provedor Codeforces

Código CF803F