Description:
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 $$\max_{i=l}^{r} a_i$$ while !Mike can instantly tell the value of $$\min_{i=l} b_i$$.
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 $$\max_{i=l}^{r}a_i = \min_{i=l}^{r}b_i$$ is satisfied.
How many occasions will the robot count?
Input Format:
The first line contains only integer n (1 ≤ n ≤ 200 000).
The second line contains n integer numbers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the sequence a.
The third line contains n integer numbers b1, b2, ..., bn ( - 109 ≤ bi ≤ 109) — the sequence b.
Output Format:
Print the only integer number — the number of occasions the robot will count, thus for how many pairs $$\max_{i=l}^{r}a_i = \min_{i=l}^{r}b_i$$ is satisfied.
Note:
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.