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 cubes 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 moving, 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.
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 the smallest number of moves. A solution will always exist.
Sample Input 1
3 2 1 1 1 1
Sample Output 1
Sample Input 2
4 3 2 2 4 4 1 1
Sample Output 2
Sample Input 3
5 8 2 2 3 2 4 2 2 4 3 4 4 4 2 3 2 3
Sample Output 3
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).