Codeforces Round 852 (Div. 2) |
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Finished |
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 $$$r$$$.
31 3 22 1 3
2
77 3 6 2 1 5 46 7 2 5 3 1 4
16
61 2 3 4 5 66 5 4 3 2 1
11
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 $$$\operatorname{MEX}(5, 4) \neq \operatorname{MEX}(1, 4)$$$.
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