Let's call a non-empty sequence of positive integers a1,a2... akcoprime 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... an (1≤ai≤100000).
Output
Print the number of coprime subsequences of a modulo 109+7.
Examples
Input
3
1 2 3
Output
5
Input
4
1 1 1 1
Output
15
Input
7
1 3 5 15 3 105 35
Output
100
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.