D. Moscow Gorillastime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputIn 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.InputThe 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.OutputPrint a single integer — the number of suitable pairs l and r.ExamplesInput
31 3 22 1 3Output
2
Input
77 3 6 2 1 5 46 7 2 5 3 1 4Output
16
Input
61 2 3 4 5 66 5 4 3 2 1Output
11
NoteIn 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).
31 3 22 1 3
2 
['binary search', 'dp', 'greedy', 'implementation', 'math', 'two pointers', '*1800']