nebuni

There are $M$ bishops placed on a chessboard with $N$ lines and $N$ columns. As we know from the game of chess, the bishops attack only on the diagonals.

A position from the chessboard is considered safe if it's not attacked by any of the bishops on the board.

Task

Write a program which finds the number of safe positions on the chessboard.

Input data

The input file nebuni.in contains on the first line the integers $N$ and $M$, separated by a space, which represent the dimensions of the chessboard, as well as the number of bishops on the chessboard. On the next $M$ lines we have the positions (line and column, separated by a space) of the $M$ bishops, each bishop's place is on a different line of the file.

Output data

The output file nebuni.out will contain a single line where a single integer will be written, representing the number of safe positions on the given chessboard.

Constraints and clarifications

• $1 \leq N \leq 10^6$
• $1 \leq M < 16 \ 500$
• The lines and columns are numbered from $1$ to $N$.
• For $50\%$ of the test cases, $N \leq 300$.
• For $60\%$ of the test cases, $M \leq 1 \ 000$.

Example

nebuni.in

5 4
2 1
1 3
4 2
5 2

nebuni.out

6

Explanation

There are $4$ bishops on the $5 \times 5$ chessboard.

The positions attacked by the $4$ bishops are colored in gray.