You are given an array a of length n. We define f_a the following way:

Initially f_a = 0, M = 1;
for every 2 ≤ i ≤ n if a_M < a_i then we set f_a = f_a + a_M and then set M = i.

Calculate the sum of f_a 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

The first line contains integer n (1 ≤ n ≤ 1 000 000) — the size of array a.

Second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

Print the only integer, the sum of f_a over all n! permutations of the array a modulo 10⁹ + 7.

Note

For the second example all the permutations are:

Where p is the array of the indices of initial array a. The sum of f_a is equal to 4.

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