Fancy Fence
time limit per test
1000 ms
memory limit per test
256 MiB
input
stdin
output
stdout

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
Copy
2
1 2
1 2
Output
Copy
12

Notes

The fence looks like this:
image

There are 5 fancy rectangles of shape:
image

There are 3 fancy rectangles of shape:
image

There is 1 fancy rectangle of shape:
image

There are 2 fancy rectangles of shape:
image

There is 1 fancy rectangle of shape:
image

Információk
Azonosító:
CEOI20_fancyfence
Cím:
Fancy Fence
Időlimit:
1000 ms
Memórialimit:
256 MiB
Tagek:
Típus:
batch

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