You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 7.0 seconds
Memory limit: 1024.0 MB

# Problem
Touko's favorite sequence of numbers is a permutation $$$a_1, a_2, \dots, a_n$$$ of $$$1, 2, \dots, n$$$, and she wants some collection of permutations that are similar to her favorite permutation.

She has a collection of $$$q$$$ intervals of the form $$$[l_i, r_i]$$$ with $$$1 \le l_i \le r_i \le n$$$. To create permutations that are similar to her favorite permutation, she coined the following definition:

- A permutation $$$b_1, b_2, \dots, b_n$$$ allows an interval $$$[l', r']$$$ to holds its shape if for any pair of integers $$$(x, y)$$$ such that $$$l' \le x < y \le r'$$$, we have $$$b_x < b_y$$$ if and only if $$$a_x < a_y$$$.
- A permutation $$$b_1, b_2, \dots, b_n$$$ is $$$k$$$-similar if $$$b$$$ allows all intervals $$$[l_i, r_i]$$$ for all $$$1 \le i \le k$$$ to hold their shapes.

Yuu wants to figure out all $$$k$$$-similar permutations for Touko, but it turns out this is a very hard task; instead, Yuu will encode the set of all $$$k$$$-similar permutations with directed acylic graphs (DAG). Yuu also coined the following definitions for herself:

- A permutation $$$b_1, b_2, \dots, b_n$$$ satisfies a DAG $$$G'$$$ if for all edge $$$u \to v$$$ in $$$G'$$$, we must have $$$b_u < b_v$$$.
- A $$$k$$$-encoding is a DAG $$$G_k$$$ on the set of vertices $$$1, 2, \dots, n$$$ such that a permutation $$$b_1, b_2, \dots, b_n$$$ satisfies $$$G_k$$$ if and only if $$$b$$$ is $$$k$$$-similar.

Since Yuu is free today, she wants to figure out the minimum number of edges among all $$$k$$$-encodings for each $$$k$$$ from $$$1$$$ to $$$q$$$.

## Input Format
The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n \le 25\,000$$$, $$$1 \le q \le 100\,000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ which form a permutation of $$$1, 2, \dots, n$$$.

The $$$i$$$-th of the following $$$q$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$. ($$$1 \le l_i \le r_i \le n$$$).

## Output Format
Print $$$q$$$ lines. The $$$k$$$-th of them should contain a single integer  — The minimum number of edges among all $$$k$$$-encodings.

## Examples
```input
4 3
2 4 1 3
1 3
2 4
1 4
```
```output
2
4
3
```
-----
```input
8 4
3 7 4 8 1 5 2 6
3 6
1 6
3 8
1 8
```
```output
3
5
9
7
```
-----
```input
10 10
10 5 1 2 7 3 9 4 6 8
2 2
4 5
6 8
4 10
4 4
2 7
2 2
7 8
3 7
2 10
```
```output
0
1
3
6
6
9
9
9
9
8
```

## Note
For the first test case:

- All $$$1$$$-similar permutations must allow the interval $$$[1, 3]$$$ to hold its shape. Therefore, the set of all $$$1$$$-similar permutations is $$$\{[3, 4, 2, 1], [3, 4, 1, 2], [2, 4, 1, 3], [2, 3, 1, 4]\}$$$. The optimal encoding of these permutations is
- All $$$2$$$-similar permutations must allow the intervals $$$[1, 3]$$$ and $$$[2, 4]$$$ to hold their shapes. Therefore, the set of all $$$2$$$-similar permutations is $$$\{[3, 4, 1, 2], [2, 4, 1, 3]\}$$$. The optimal encoding of these permutations is
- All $$$3$$$-similar permutations must allow the intervals $$$[1, 3]$$$, $$$[2, 4]$$$, and $$$[1, 4]$$$ to hold their shapes. Therefore, the set of all $$$3$$$-similar permutations only includes $$$[2, 4, 1, 3]$$$. The optimal encoding of this permutation is

Now solve the problem and return the code.