A. Fancy Fencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputEverybody 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 ith 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.InputThe first line contains N (1\leq N \leq 10^{5}) – the number of sections.  The second line contains N space-separated integers, the ith number is h_i (1 \leq h_i \leq 10^{9}).  The third line contains N space-separated integers, the ith number is w_i (1 \leq w_i \leq 10^{9}).OutputYou 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} ExampleInput
2
1 2
1 2
Output
12
NoteThe 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:  
2
1 2
1 2

12 
['*special problem', 'data structures', 'dsu', 'implementation', 'math', 'sortings', '*1800']