You are given a complete graph with \(n\) nodes. There are two values associated with each node \(i\), denoted by \(a_i\) and \(b_i\).

The weight of the edge between two nodes \(i\) and \(j\) is denoted by \(w_{ij} = |a_ib_j-a_jb_i|\).

Find the sum of the square of weights of all the edges. Formally, find the value \(\sum_\limits{i=1}^n\sum_\limits{j=i+1}^nw_{ij}^2\).

Input format

• The first line contains a single integer \(n\).
• The second line contains \(n\) space-separated integers \(a_1,a_2,...,a_n\).
• The third line contains \(n\) space-separated integers \(b_1,b_2,...,b_n\).

Output format

Print a single integer denoting the required value (mod \(10^9+7\)).

Constraints