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

$2\le n\le 10^6\\-10^{15}\le a_i,b_i\le 10^{15}$