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D. Friends and Subsequences

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputMike 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?

Input

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

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*.

Output

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

Examples

Input

6

1 2 3 2 1 4

6 7 1 2 3 2

Output

2

Input

3

3 3 3

1 1 1

Output

0

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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