Everybody knows that Balázs has the fanciest fence in the whole town. It's built up from $N$ fancy sections. The sections are rectangles standing closely next to each other on the ground. The $i$th section has integer height $h_i$ and integer width $w_i$. We are looking for fancy rectangles on this fancy fence. A rectangle is fancy if:

• its sides are either horizontal or vertical and have integer lengths
• the distance between the rectangle and the ground is integer
• the distance between the rectangle and the left side of the first section is integer
• it's lying completely on sections

The first line contains $N$ ($1\leq N \leq 10^{5}$) – the number of sections. The second line contains $N$ space-separated integers, the $i$th number is $h_i$ ($1 \leq h_i \leq 10^{9}$). The third line contains $N$ space-separated integers, the $i$th number is $w_i$ ($1 \leq w_i \leq 10^{9}$).

You should print a single integer, the number of fancy rectangles modulo $10^9+7$. So the output range is $0,1,2,\ldots, 10^9+6$.

Scoring