F. Optimal Encodingtime limit per test7 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputTouko'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.InputThe 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).OutputPrint q lines. The k-th of them should contain a single integer  — The minimum number of edges among all k-encodings.ExamplesInput
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
NoteFor 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  
4 3
2 4 1 3
1 3
2 4
1 4

2 4 3 
['brute force', 'data structures', '*3500']