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

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

The second line contains n integer numbers a1,a2... an (1 \le ai \le 100000).

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

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.