In the nearby kindergarten they recently made up an attractive game of strength and agility that kids love.

The surface for the game is a large flat area divided into $N \times N$ squares.

The children lay large spongy cues onto the surface. The sides of the cubes are the same length as the sides of the squares. When a cube is put on the surface, its sides are aligned with some square. A cube may be put on another cube too.

Kids enjoy building forts and hiding them, but they always leave behind a huge mess. Because of this, prior to closing the kindergarten, the teachers rearrange all the cubes so that they occupy a rectangle on the surface, with exactly one cube on every square in the rectangle.

In one move, a cube is taken off the top of a square to the top of any other square.

Write a program that, given the state of the surface, calculates the smallest number of moves needed to arrange all cubes into a rectangle.

-----Input-----
The first line contains the integers $N$ and $M$ ($1 \le N \le 100$, $1 \le M \le N^2$), the dimensions of the surface and the number of cubes currently on the surface.

Each of the following $M$ lines contains two integers $R$ and $C$ ($1 \le R, C \le N$), the coordinates of the square that contains the cube.

-----Output-----
Output the smallest number of moves. A solution will always exist.

-----Explanation of Sample Data-----
In the first example, it suffices to move one of the cubes from $(1, 1)$ to $(1, 2)$ or $(2, 1)$.

In the third example, a cube is moved from $(2, 3)$ to $(3, 3)$, from $(4, 2)$ to $(2, 5)$ and from $(4, 4)$ to $(3, 5)$.

-----Examples-----
Sample Input 1:
3 2
1 1
1 1
Sample Output 1:
1

Sample Input 2:
4 3
2 2
4 4
1 1
Sample Output 2:
2

Source: kattis | Difficulty: MEDIUM


Solutions: