A10375. Friends and Subsequences

Mike and !Mike are old childhood rivals, they are opposite in everything they do, except programming. Today they have a problem they cannot solve on their own, but together (with you) — who knows?

Every one of them has an integer sequences $a$ and $b$ of length $n$ . Being given a query of the form of pair of integers $(l,r)$ , Mike can instantly tell the value of  while !Mike can instantly tell the value of .

Now suppose a robot (you!) asks them all possible different queries of pairs of integers $(l,r)$ $(1<=l<=r<=n)$ (so he will make exactly $n(n+1)/2$ queries) and counts how many times their answers coincide, thus for how many pairs  is satisfied.

How many occasions will the robot count?

The first line contains only integer $n$ ( $1<=n<=200000$ ).

The second line contains $n$ integer numbers $a_{1},a_{2},...,a_{n}$ ( $-10^{9}<=a_{i}<=10^{9}$ ) — the sequence $a$ .

The third line contains $n$ integer numbers $b_{1},b_{2},...,b_{n}$ ( $-10^{9}<=b_{i}<=10^{9}$ ) — the sequence $b$ .

Print the only integer number — the number of occasions the robot will count, thus for how many pairs  is satisfied.

The occasions in the first sample case are:

1\. $l=4$ , $r=4$ since $max{2}=min{2}$ .

2\. $l=4$ , $r=5$ since $max{2,1}=min{2,3}$ .

There are no occasions in the second sample case since Mike will answer $3$ to any query pair, but !Mike will always answer $1$ .