You are given an array \(A\) of \(N\) integers. For every index \(i\) of the array \(A\), you need to select an index \(j\) such that \(j \neq i \) and the product of \(A[i]\) and \(A[j]\) is maximum for that \(i\) . Finally, you need to print the sum of \(A[i] * A[j]\) for all the indices \(i\) . Since this sum can be large, you need to print it to the modulo \(10^9 + 7\).
Note: Please refer to the sample explanation section.

Input format

First line: Integer \(N\) denoting the number of elements in the array \(A\)
Next line: \(N\) space-separated integers denoting the elements of the array \(A\)

Output format

Print the required sum to the modulo \(10^9+7\).

Constraints
\(2 \le N \le 10^5 \)

\(-10^{18} \le A[i] \le 10^{18}\)