1648: CF803 - F. Coprime Subsequences
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Description
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputLet'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].
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