Dirigent

Winter school of informatics ends with a traditional dance. There are $n$ students who participate. Each of them has a unique label between $1$ and $n$.

First, conductor Krešo orders the students to form a circle such that each student holds hands with two other students.

Alenka is wondering if it is possible to break the circle by making exactly one pair of neighbouring students stop holding hands and that the newly formed sequence of students is sorted by their labels. For example, if their order is 3 4 1 2, then the circle can be broken between students with labels 4 and 1. If their order is 2 1 4 3, then there is no way to break the circle in such a way.

During the night Krešo is going to give $q$ instructions. In each of them, he orders two students to swap places. After each swap, you need to help Alenka answer her question.

The first line contains two integers $n$ and $q$ ($1 ≤ n, q ≤ 300000$), the number of students and the number of swaps.

The second line contains $n$ integers $a_i$ ($1 ≤ a_i ≤ n$), describing the initial placement of students in the circle.

In each of the next $q$ lines there are two integers $x_i$, $y_i$ ($1 ≤ x_i, y_i ≤ n$, $x_i ≠ y_i$), describing Krešo's $i$-th instruction. Students with labels $x_i$ and $y_i$ swap places.

In the $i$-th of the $q$ lines, output the answer after the first $i$ swaps have been carried out. Print DA if the answer is yes, otherwise print NE.

Clarification of the second example: the students at the beginning, after the first swap, and after the second swap.