A11774 | Good Subsegments

A permutation $p$ of length $n$ is a sequence $p_1, p_2, \ldots, p_n$ consisting of $n$ distinct integers, each of which from $1$ to $n$ ( $1 \leq p_i \leq n$ ) .

Let's call the subsegment $[l,r]$ of the permutation good if all numbers from the minimum on it to the maximum on this subsegment occur among the numbers $p_l, p_{l+1}, \dots, p_r$ .

For example, good segments of permutation $[1, 3, 2, 5, 4]$ are:

- $[1, 1]$ ,
- $[1, 3]$ ,
- $[1, 5]$ ,
- $[2, 2]$ ,
- $[2, 3]$ ,
- $[2, 5]$ ,
- $[3, 3]$ ,
- $[4, 4]$ ,
- $[4, 5]$ ,
- $[5, 5]$ .

You are given a permutation $p_1, p_2, \ldots, p_n$ .

You need to answer $q$ queries of the form: find the number of good subsegments of the given segment of permutation.

In other words, to answer one query, you need to calculate the number of good subsegments $[x \dots y]$ for some given segment $[l \dots r]$ , such that $l \leq x \leq y \leq r$ .

The first line contains a single integer $n$ ( $1 \leq n \leq 120000$ ) — the number of elements in the permutation.

The second line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ separated by spaces ( $1 \leq p_i \leq n$ ).

The third line contains an integer $q$ ( $1 \leq q \leq 120000$ ) — number of queries.

The following $q$ lines describe queries, each line contains a pair of integers $l$ , $r$ separated by space ( $1 \leq l \leq r \leq n$ ).

Print a $q$ lines, $i$ -th of them should contain a number of good subsegments of a segment, given in the $i$ -th query.