B"Lee couldn't sleep lately, because he had nightmares. In one of his nightmares (which was about an unbalanced global round), he decided to fight back and propose a problem below (which you should solve) to balance the round, hopefully setting him free from the nightmares. A non-empty array b_1, b_2, ldots, b_m is called good, if there exist m integer sequences which satisfy the following properties: You are given an array a_1, a_2, ldots, a_n . It has 2^n - 1 nonempty subsequences. Find how many of them are good. As this number can be very large, output it modulo 10^9 + 7 . An array c is a subsequence of an array d if c can be obtained from d by deletion of several (possibly, zero or all) elements. The first line contains a single integer n ( 2 <= n <= 2 cdot 10^5 ) -- the size of array a . The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^9 ) -- elements of the array. Print a single integer -- the number of nonempty good subsequences of a , modulo 10^9 + 7 . For the first test, two examples of good subsequences are [2, 7] and [2, 2, 4, 7] : For b = [2, 7] we can use (-3, -4) as the first sequence and (-2, -1, ldots, 4) as the second. Note that subsequence [2, 7] appears twice in [2, 2, 4, 7] , so we have to count it twice. For b = [2, 2, 4, 7] the following sequences would satisfy the properties: (-1, 0) , (-3, -2) , (0, 1, 2, 3) and (-3, -2, ldots, 3) "...