B. Cells Not Under Attack

time limit per test2 seconds

memory limit per test256 megabytes

inputstandard input

outputstandard output

Vasya has the square chessboard of size n × n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.

The cell of the field is under rook's attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.

You are given the positions of the board where Vasya will put   rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, n2)) — the size of the board and the number of rooks.

Each of the next m lines contains integers xi and yi (1 ≤ xi, yi ≤ n) — the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.

Output

Print m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.

Examples

input

3 3

1 1

3 1

2 2

output

4 2 0 

input

5 2

1 5

5 1

output

16 9 

input

100000 1

300 400

output

9999800001 

Note

On the picture below show the state of the board after put each of the three rooks. The cells which painted with grey color is not under the attack.

题意：在田野里面放秃鹫，每个可以使这一个秃鹫的一行和一列under the attack。求每放一个还剩几个没有under the attack;

思路：当放入的行或者列已经有秃鹫就不需要在加上那一行，当放入的行和列与其他秃鹫所在行和列会 相交。

 

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