Max to the Right of Min

3000ms

262144K

Description:

You are given a permutation $$$p$$$ of length $$$n$$$ — an array, consisting of integers from $$$1$$$ to $$$n$$$, all distinct.

Let $$$p_{l,r}$$$ denote a subarray — an array formed by writing down elements from index $$$l$$$ to index $$$r$$$, inclusive.

Let $$$\mathit{maxpos}_{l,r}$$$ denote the index of the maximum element on $$$p_{l,r}$$$. Similarly, let $$$\mathit{minpos}_{l,r}$$$ denote the index of the minimum element on it.

Calculate the number of subarrays $$$p_{l,r}$$$ such that $$$\mathit{maxpos}_{l,r} > \mathit{minpos}_{l,r}$$$.

Input:

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the number of elements in the permutation.

The second line contains $$$n$$$ integers $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$). All $$$p_i$$$ are distinct.

Output:

Print a single integer — the number of subarrays $$$p_{l,r}$$$ such that $$$\mathit{maxpos}_{l,r} > \mathit{minpos}_{l,r}$$$.

Sample Input:

3
1 2 3

Sample Output:

Sample Input:

6
5 3 6 1 4 2

Sample Output:

Sample Input:

10
5 1 6 2 8 3 4 10 9 7

Sample Output:

Informação

Provedor Codeforces

Código CF1849E