B"Pussycat Sonya has an array consisting of n positive integers. There are 2n possible subsequences of the array. For each subsequence she counts the minimum number of operations to make all its elements equal. Each operation must be one of two: What is the sum of minimum number of operations for all 2n possible subsequences? Find and print this sum modulo 109 xe2 x80 x89+ xe2 x80 x897. The first line of the input contains a single integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89300 xe2 x80 x89000) -- the size of the array. The second line contains n integers t1, xe2 x80 x89t2, xe2 x80 x89..., xe2 x80 x89tn (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ti xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89300 xe2 x80 x89000) -- elements of the array. Print the sum of minimum number of operation for all possible subsequences of the given array modulo 109 xe2 x80 x89+ xe2 x80 x897. In the first sample, there are 8 possible subsequences: (60, xe2 x80 x8960, xe2 x80 x8940), (60, xe2 x80 x8960), (60, xe2 x80 x8940), (60, xe2 x80 x8940), (60), (60), (40) and () (empty subsequence). For a subsequence (60, xe2 x80 x8960, xe2 x80 x8940) we can make all elements equal by two operations -- divide 40 by 2 to get 20, and then multiply 20 by 3 to get 60. It's impossible to achieve the goal using less operations and thus we add 2 to the answer. There are two subsequences equal to (60, xe2 x80 x8940) and for each of them the also need to make at least 2 operations. In each of other subsequences all numbers are already equal, so we need 0 operations for each of them. The sum is equal to 2 xe2 x80 x89+ xe2 x80 x892 xe2 x80 x89+ xe2 x80 x892 xe2 x80 x89= xe2 x80 x896. "...