Problem: Touko's favorite sequence of numbers is a permutation a_1, a_2, ..., a_n of 1, 2, ..., 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 ≤ l_i ≤ r_i ≤ n. To create permutations that are similar to her favorite permutation, she coined the following definition:

  * A permutation b_1, b_2, ..., b_n allows an interval [l', r'] to holds its shape if for any pair of integers (x, y) such that l' ≤ x < y ≤ r', we have b_x < b_y if and only if a_x < a_y. 
  * A permutation b_1, b_2, ..., b_n is k-similar if b allows all intervals [l_i, r_i] for all 1 ≤ i ≤ 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, ..., b_n satisfies a DAG G' if for all edge u → 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, ..., n such that a permutation b_1, b_2, ..., 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

The first line contains two integers n and q (1 ≤ n ≤ 25 000, 1 ≤ q ≤ 100 000).

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

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

Output

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 <image>
  * 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 <image>
  * 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 <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using std::cin;
using std::cout;

const int N = 25400, M = N * 4;

int n, m, ans;
int p[N], lm[N];
int lpre[N], lsuf[N], rpre[N], rsuf[N];

inline void linkA(int l, int r) {rsuf[l] = r, lpre[r] = l, ++ans;}
inline void linkD(int l, int r) {rpre[l] = r, lsuf[r] = l, ++ans;}
inline void cutA(int l, int r) {ans -= rsuf[l] == r && lpre[r] == l;}
inline void cutD(int l, int r) {ans -= rpre[l] == r && lsuf[r] == l;}

inline void update(int l, int r) {
	if (p[l] < p[r]) {
		if (p[l] > p[lpre[r]]) cutA(l, rsuf[l]), cutA(lpre[r], r), linkA(l, r);
	} else {
		if (p[r] > p[rpre[l]]) cutD(l, rpre[l]), cutD(lsuf[r], r), linkD(l, r);
	}
}

int main() {
	int i, l, r;
	std::ios::sync_with_stdio(false), cin.tie(nullptr);
	cin >> n >> m;
	for (i = 1; i <= n; ++i) cin >> p[i], lm[i] = i;
	for (; m; --m) {
		cin >> l >> r, i = std::upper_bound(lm + 1, lm + (n + 1), l) - lm;
		for (; i <= r; ++i) for (; lm[i] > l; update(--lm[i], i));
		cout << ans << '\n';
	}
	return 0;
}