CF1793D Moscow Gorillas

In winter, the inhabitants of the Moscow Zoo are very bored, in particular, it concerns gorillas. You decided to entertain them and brought a permutation $ p $ of length $ n $ to the zoo. A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in any order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ occurs twice in the array) and $ [1,3,4] $ is also not a permutation ( $ n=3 $ , but $ 4 $ is present in the array). The gorillas had their own permutation $ q $ of length $ n $ . They suggested that you count the number of pairs of integers $ l, r $ ( $ 1 \le l \le r \le n $ ) such that $ \operatorname{MEX}([p_l, p_{l+1}, \ldots, p_r])=\operatorname{MEX}([q_l, q_{l+1}, \ldots, q_r]) $ . The $ \operatorname{MEX} $ of the sequence is the minimum integer positive number missing from this sequence. For example, $ \operatorname{MEX}([1, 3]) = 2 $ , $ \operatorname{MEX}([5]) = 1 $ , $ \operatorname{MEX}([3, 1, 2, 6]) = 4 $ . You do not want to risk your health, so you will not dare to refuse the gorillas.

The first line contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the permutations length. The second line contains $ n $ integers $ p_1, p_2, \ldots, p_n $ ( $ 1 \le p_i \le n $ ) — the elements of the permutation $ p $ . The third line contains $ n $ integers $ q_1, q_2, \ldots, q_n $ ( $ 1 \le q_i \le n $ ) — the elements of the permutation $ q $ .

Print a single integer — the number of suitable pairs $ l $ and $ r $ .

In the first example, two segments are correct – $ [1, 3] $ with $ \operatorname{MEX} $ equal to $ 4 $ in both arrays and $ [3, 3] $ with $ \operatorname{MEX} $ equal to $ 1 $ in both of arrays. In the second example, for example, the segment $ [1, 4] $ is correct, and the segment $ [6, 7] $ isn't correct, because $ \operatorname{MEX}(5, 4) \neq \operatorname{MEX}(1, 4) $ .