B'Petya was late for the lesson too. The teacher gave him an additional task. For some array a Petya should find the number of different ways to select non-empty subset of elements from it in such a way that their product is equal to a square of some integer. Two ways are considered different if sets of indexes of elements chosen by these ways are different. Since the answer can be very large, you should find the answer modulo 109 xe2 x80 x89+ xe2 x80 x897. First line contains one integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105) -- the number of elements in the array. Second line contains n integers ai (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x8970) -- the elements of the array. Print one integer -- the number of different ways to choose some elements so that their product is a square of a certain integer modulo 109 xe2 x80 x89+ xe2 x80 x897. In first sample product of elements chosen by any way is 1 and 1 xe2 x80 x89= xe2 x80 x8912. So the answer is 24 xe2 x80 x89- xe2 x80 x891 xe2 x80 x89= xe2 x80 x8915. In second sample there are six different ways to choose elements so that their product is 4, and only one way so that their product is 16. So the answer is 6 xe2 x80 x89+ xe2 x80 x891 xe2 x80 x89= xe2 x80 x897. '...