CF701B.Cells Not Under Attack

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.

瓦西娅有一个 $n \times n$ 的正方形棋盘和 $m$ 个车（rook）。初始时棋盘为空。瓦西娅将依次把这 $m$ 个车逐一放置到棋盘上。

若某个格子与至少一个车位于同一行或同一列，则该格子处于车的攻击范围内；若某个格子上本身就有车，那么该格子也视为处于攻击范围内。

现给出瓦西娅放置车的位置序列。对每一个被放置的车，请你计算：在它被放上棋盘之后，棋盘上未被任何车攻击的格子数量。

The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, _n_2)) — the size of the board and the number of rooks.

Each of the next m lines contains integers x__i and y__i (1 ≤ x__i, y__i ≤ 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.

输入的第一行包含两个整数 $n$ 和 $m$（$1 ≤ n ≤ 100\,000$，$1 ≤ m ≤ \min(100\,000,\,n^2)$）—— 分别表示棋盘的大小和车的数量。

接下来的 $m$ 行中，每行包含两个整数 $x_i$ 和 $y_i$（$1 ≤ x_i,\,y_i ≤ n$）—— 表示第 $i$ 个车将被放置在第 $x_i$ 行、第 $y_i$ 列。瓦夏按照输入中出现的顺序依次在棋盘上放置车。保证任意一个格子至多放置一个车。

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.

输出 $m$ 个整数，其中第 $i$ 个整数应等于在放置前 $i$ 个车之后未被攻击的格子数量。

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.

下图展示了依次放置三个车后棋盘的状态。灰色涂色的格子表示未被攻击的格子。