P6801 [CEOI 2020] Fancy Fence.

0.1 s, 32 MB.

As everyone knows, Balázs has the most beautiful fence in the whole town. The fence consists of $N$ sections. Each section is a rectangle, and any two adjacent sections are tightly connected. The $i$-th rectangle has height $h_i$ and width $w_i$. We need to find “fancy rectangles” that satisfy the following conditions: - Each side of the rectangle is horizontal or vertical, and the length of each side is an integer. - The distance from the rectangle to the ground is an integer. - The distance from the rectangle to the left side of the first section of the fence is an integer. - The rectangle is completely contained within the fence. Now you need to compute the total number of fancy rectangles. Since this number may be very large, output it modulo $10^9+7$.

The first line contains an integer $N$, meaning the fence consists of $N$ sections. The second line contains $N$ integers. The $i$-th integer is the height $h_i$ of the $i$-th rectangle. The third line contains $N$ integers. The $i$-th integer is the width $w_i$ of the $i$-th rectangle.

Output the number of fancy rectangles modulo $10^9+7$.

### Sample Explanation 1 The shape of the fence is as shown below:  There are $5$ rectangles of the following shape:  There are $3$ rectangles of the following shape:  There is $1$ rectangle of the following shape:  There are $2$ rectangles of the following shape:  There is $1$ rectangle of the following shape:  ### Sample 2 See the additional file. ### Subtasks All test points satisfy: $1 \leq N \leq 10^5$, $1 \leq h_i,w_i \leq 10^9$. The constraints for each subtask are as follows: | Subtask ID | Score | Constraints | | ---------- | ----- | ----------- | | $1$ | $0$ | Samples | | $2$ | $12$ | $N \leq 50$, and $\forall i \in [1,N]$, $h_i \leq 50$ and $w_i=1$ | | $3$ | $13$ | $\forall i \in [1,N]$, $h_i=1$ or $h_i=2$ | | $4$ | $15$ | All $h_i$ are equal | | $5$ | $15$ | $\forall i \in [1,N-1]$, $h_i \leq h_{i+1}$ | | $6$ | $18$ | $N \leq 1000$ | | $7$ | $27$ | No special constraints | Translated by ChatGPT 5