#include<bits/stdc++.h>
using namespace std;
#define Re register int

const int N = 25005;
int n, m, ans, a[N], d[N], lpre[N], lsuf[N], rpre[N], rsuf[N];

inline int read()
{
	char c = getchar();
	int ans = 0;
	while (c < 48 || c > 57) c = getchar();
	while (c >= 48 && c <= 57) ans = (ans << 3) + (ans << 1) + (c ^ 48), c = getchar();
	return ans;
}

inline void write(int x)
{
	int num = 0;
	char sc[15];
	if (!x) sc[num = 1] = 48;
	while (x) sc[++num] = x % 10 + 48, x /= 10;
	while (num) putchar(sc[num--]);
	putchar('\n');
}

inline void add1(int x, int y)
{
	++ans, rsuf[x] = y, lpre[y] = x;
}

inline void add2(int x, int y)
{
	++ans, rpre[x] = y, lsuf[y] = x;
}

inline void cut1(int x, int y)
{
	ans -= (rsuf[x] == y && lpre[y] == x);
}

inline void cut2(int x, int y)
{
	ans -= (rpre[x] == y && lsuf[y] == x);
}

inline void calc(int x, int y)
{
	if (a[x] < a[y])
	{
		if (a[x] > a[lpre[y]]) cut1(lpre[y], y), cut1(x, rsuf[x]), add1(x, y);
	}
	else
	{
		if (a[x] < a[lsuf[y]]) cut2(lsuf[y], y), cut2(x, rpre[x]), add2(x, y);
	}
}

int main()
{
	n = read(), m = read(), a[n + 1] = n + 1;
	for (Re i = 1; i <= n; ++i) a[i] = read(), d[i] = i, lsuf[i] = rsuf[i] = n + 1;
	while (m--)
	{
		int u = read(), v = read();
		int l = u, r = v, s = v + 1;
		while (l <= r)
		{
			int mid = l + r >> 1;
			if (d[mid] > u) s = mid, r = mid - 1;
			else l = mid + 1;
		}
		for (Re i = s; i <= v; ++i)
			while (d[i] > u) calc(--d[i], i);
		write(ans);
	}
	return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define Re register int

const int N = 25005;
int n, m, ans, a[N], d[N], lpre[N], lsuf[N], rpre[N], rsuf[N];

inline int read()
{
	char c = getchar();
	int ans = 0;
	while (c < 48 || c > 57) c = getchar();
	while (c >= 48 && c <= 57) ans = (ans << 3) + (ans << 1) + (c ^ 48), c = getchar();
	return ans;
}

inline void write(int x)
{
	int num = 0;
	char sc[15];
	if (!x) sc[num = 1] = 48;
	while (x) sc[++num] = x % 10 + 48, x /= 10;
	while (num) putchar(sc[num--]);
	putchar('\n');
}

inline void add1(int x, int y)
{
	++ans, rsuf[x] = y, lpre[y] = x;
}

inline void add2(int x, int y)
{
	++ans, rpre[x] = y, lsuf[y] = x;
}

inline void cut1(int x, int y)
{
	ans -= (rsuf[x] == y && lpre[y] == x);
}

inline void cut2(int x, int y)
{
	ans -= (rpre[x] == y && lsuf[y] == x);
}

inline void calc(int x, int y)
{
	if (a[x] < a[y])
	{
		if (a[x] > a[lpre[y]]) cut1(lpre[y], y), cut1(x, rsuf[x]), add1(x, y);
	}
	else
	{
		if (a[x] < a[lsuf[y]]) cut2(lsuf[y], y), cut2(x, rpre[x]), add2(x, y);
	}
}

int main()
{
	n = read(), m = read(), a[n + 1] = n + 1;
	for (Re i = 1; i <= n; ++i) a[i] = read(), d[i] = i, lsuf[i] = rsuf[i] = n + 1;
	while (m--)
	{
		int u = read(), v = read();
		int l = u, r = v, s = v + 1;
		while (l <= r)
		{
			int mid = l + r >> 1;
			if (d[mid] > u) s = mid, r = mid - 1;
			else l = mid + 1;
		}
		for (Re i = s; i <= v; ++i)
			while (d[i] > u) calc(--d[i], i);
		write(ans);
	}
	return 0;
}

```