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 $\text{[math]}$ while !Mike can instantly tell the value of $\text{[math]}$ .

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 $\text{[math]}$ is satisfied.

How many occasions will the robot count?

Input

The first line contains only integer n (1 ≤ n ≤ 200 000).

The second line contains n integer numbers a₁, a₂, ..., a_n ( - 10⁹ ≤ a_i ≤ 10⁹) — the sequence a.

The third line contains n integer numbers b₁, b₂, ..., b_n ( - 10⁹ ≤ b_i ≤ 10⁹) — the sequence b.

Output

Print the only integer number — the number of occasions the robot will count, thus for how many pairs $\text{[math]}$ 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.

Friends and Subsequences

Examples