Friends and Subsequences

题意翻译

- 给定序列 $a$ 和序列 $b$，长度均为 $n$。问有多少组 $(l,r)$，满足 $1\le l\le r\le n$ 且 $$\max_{i=l}^r a_i=\min_{i=l}^r b_i$$ - $1\le n\le 2\times 10^5$，$|a_i|,|b_i|\le 10^9$。

题目描述

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?

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

6
1 2 3 2 1 4
6 7 1 2 3 2

输出样例 #1

2

输入样例 #2

3
3 3 3
1 1 1

输出样例 #2

0

说明

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 $ .