CF938E.Max History

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 $10^{9}+7$ .

Note: two elements are considered different if their indices differ, so for every array $a$ there are exactly $n!$ permutations.

The first line contains integer $n$ ( $1<=n<=1\ 000\ 000$ ) — the size of array $a$ .

Second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ).

Print the only integer, the sum of $f_{a}$ over all $n!$ permutations of the array $a$ modulo $10^{9}+7$ .

For the second example all the permutations are:

• $p=[1,2,3]$ : $f_{a}$ is equal to $1$ ;
• $p=[1,3,2]$ : $f_{a}$ is equal to $1$ ;
• $p=[2,1,3]$ : $f_{a}$ is equal to $1$ ;
• $p=[2,3,1]$ : $f_{a}$ is equal to $1$ ;
• $p=[3,1,2]$ : $f_{a}$ is equal to $0$ ;
• $p=[3,2,1]$ : $f_{a}$ is equal to $0$ .

Where $p$ is the array of the indices of initial array $a$ . The sum of $f_{a}$ is equal to $4$ .