D. Moscow Gorillas
binary search; dp; greedy; implementation; math; two pointers
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 \(\operatorname{MEX}(5, 4) \neq \operatorname{MEX}(1, 4)\).