E. Max Historytime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputPrint the only integer, the sum of fa over all n! permutations of the array a modulo 109 + 7.ExamplesInput21 3Output1Input31 1 2Output4NoteFor 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.
Input21 3
Output1
['combinatorics', 'math', '*2300']