A. Fancy Fence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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
What is the number of fancy rectangles? This number can be very big, so we are interested in it modulo $10^9+7$.
Input

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 $w_i$ ($1 \leq w_i \leq 10^{9}$).

Output

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
$\begin{array}{|c|c|c|} \hline \text{Subtask} & \text{Points} & \text{Constraints} \\ \hline 1 & 0 & \text{sample}\\ \hline 2 & 12 & N \leq 50 \: \text{and} \: h_i \leq 50 \: \text{and} \: w_i = 1 \: \text{for all} \: i \\ \hline 3 & 13 & h_i = 1 \: \text{or} \: h_i = 2 \: \text{for all} \: i \\ \hline 4 & 15 & \text{all} \: h_i \: \text{are equal} \\ \hline 5 & 15 & h_i \leq h_{i+1} \: \text{for all} \: i \leq N-1 \\ \hline 6 & 18 & N \leq 1000\\ \hline 7 & 27 & \text{no additional constraints}\\ \hline \end{array}$
Example
Input
2
1 2
1 2

Output
12

Note

The fence looks like this:

There are 5 fancy rectangles of shape:

There are 3 fancy rectangles of shape:

There is 1 fancy rectangle of shape:

There are 2 fancy rectangles of shape:

There is 1 fancy rectangle of shape: