Fred Lever just learned that knights in Chess are very good at forking, which is when they attack multiple pieces simultaneously. To practice this skill, he uses a ~N~ by ~N~ board with ~M~ rooks on it. For simplicity, the top-left cell is denoted as ~(1, 1)~ and the bottom-right as ~(N, N)~. Every rook is placed on a distinct cell ~(r_i, r_j)~ on the board. Fred wants to know how many cells he can place a knight on the board that forks two or more rooks, without the knight being attacked (or on the same cell of a rook).

Remember, knights in Chess may move from a cell ~(x, y)~ to cells ~(x \pm 1, y \pm 2)~ or cells ~(x \pm 2, y \pm 1)~ and rooks may move from a cell ~(x, y)~ to cells ~(x+k, y)~ or cells ~(x, y+k)~ where ~k~ is a nonzero integer. However, all pieces must stay on the board.

.....
.....
.R.R.
.....
..K..

The above figure is an example of a knight (K) forking two rooks (R) on a ~5~ by ~5~ board. Note that the knight can also fork the rooks if it were placed at ~(1, 3)~.

Constraints

For all subtasks,

~2 \le N \le 10^9~

~2 \le M < \min(10^5, N^2)~

~1 \le r_i, r_j \le N~

all ~(r_i, r_j)~ are pairwise distinct.

Subtask 1 [25%]

~2 \le N \le 2 \times 10^3~

Subtask 2 [75%]

No additional constraints.

Input Specification

The first line will contain two integers ~N~ and ~M~, space-separated.

The next ~M~ lines will contain two integers ~r_i~ and ~r_j~, denoting the location of a rook on the board.

Sample Input 1

5 2
3 2
3 4

Sample Output 1

2

Explanation for Sample Output 1

This is the example in the problem statement.

Sample Input 2

6 4
4 3
4 5
4 1
3 4

Sample Output 2

3

Explanation for Sample Output 2

......
.K...K
...R..
R.R.R.
......
.K....

The above figure shows where knights can be placed to fork two or more rooks. Note that ~(6, 4)~ is not a valid cell as the knight would be attacked by the rook on ~(3, 4)~.