第一行包含两个空格分隔的整数 n 和 m （2≤n≤1000， 0≤m≤105） - 字段的大小和禁止单元格的数量。接下来的 m 行各包含两个空格分隔的整数。具体来说，这些行的第 i 条包含数字 x i 和 y i （1≤x i，y i≤n） − 第 i 个禁止单元格的坐标。所有给定的单元格都是不同的。
考虑从上到下从 1 到 n 编号的字段行，以及从左到右从 1 到 n 的列 −。
Gerald plays the following game. He has a checkered field of size n×n cells, where m various cells are banned. Before the game, he has to put a few chips on some border (but not corner) board cells. Then for n-1 minutes, Gerald every minute moves each chip into an adjacent cell. He moves each chip from its original edge to the opposite edge. Gerald loses in this game in each of the three cases:
At least one of the chips at least once fell to the banned cell.
At least once two chips were on the same cell.
At least once two chips swapped in a minute (for example, if you stand two chips on two opposite border cells of a row with even length, this situation happens in the middle of the row).
In that case he loses and earns 0 points. When nothing like that happened, he wins and earns the number of points equal to the number of chips he managed to put on the board. Help Gerald earn the most points.
Input
The first line contains two space-separated integers n and m (2≤n≤1000, 0≤m≤105) − the size of the field and the number of banned cells. Next m lines each contain two space-separated integers. Specifically, the i-th of these lines contains numbers xi and yi (1≤xi,yi≤n) − the coordinates of the i-th banned cell. All given cells are distinct.
Consider the field rows numbered from top to bottom from 1 to n, and the columns − from left to right from 1 to n.
Output
Print a single integer − the maximum points Gerald can earn in this game.
Examples
Input
3 1
2 2
Output
0
Input
3 0
Output
1
Input
4 3
3 1
3 2
3 3
Output
1
Note
In the first test the answer equals zero as we can't put chips into the corner cells.
In the second sample we can place one chip into either cell (1, 2), or cell (3, 2), or cell (2, 1), or cell (2, 3). We cannot place two chips.
In the third sample we can only place one chip into either cell (2, 1), or cell (2, 4).