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 $l' \le x \lt y \le r'$, we have $b_x \lt b_y$ if and only if $a_x \lt a_y$.
• 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 $b_u \lt b_v$.
• 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

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

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

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