Description: You are given an array a of length n. We define fa the following way: - Initially fa = 0, M = 1; - for every 2 ≤ i ≤ n if aM < ai then we set fa = fa + aM and then set M = i. Calculate the sum of fa over all n! permutations of the array a modulo 109 + 7. Note: two elements are considered different if their indices differ, so for every array a there are exactly n! permutations. Input Format: The first line contains integer n (1 ≤ n ≤ 1 000 000) — the size of array a. Second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109). Output Format: Print the only integer, the sum of fa over all n! permutations of the array a modulo 109 + 7. Note: For the second example all the permutations are: - p = [1, 2, 3] : fa is equal to 1; - p = [1, 3, 2] : fa is equal to 1; - p = [2, 1, 3] : fa is equal to 1; - p = [2, 3, 1] : fa is equal to 1; - p = [3, 1, 2] : fa is equal to 0; - p = [3, 2, 1] : fa is equal to 0. Where p is the array of the indices of initial array a. The sum of fa is equal to 4.