CF1849E.Max to the Right of Min

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 $\mathit{maxpos}_{l,r} > \mathit{minpos}_{l,r}$ .

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.

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