Space is represented as a ~3~-dimensional ~N \times N \times N~ cube where each coordinate is between ~1~ and ~N~, and is a dangerous place. You are riding a spaceship and want to take a nap at some positive integer coordinate ~(a, b, c)~. However, your spaceship has identified ~M~ threats across space, each at positive integer coordinates ~(x_i, y_i, z_i)~. Multiple threats may be at the same coordinate.

The safety value at a coordinate is the sum of the manhattan distances from the coordinate to each threat. Formally, the safety value at ~(a, b, c)~ is:

$$\displaystyle \sum\limits_{i=1}^M |a-x_i|+|b-y_i|+|c-z_i| $$

You want to nap as safely as possible. Can you find the maximum safety value of a coordinate in space?

Constraints

~1 \le N \le 10^9~

~1 \le M \le 10^5~

~1 \le x, y, z \le N~

Subtask 1 [35%]

~1 \le N, M \le 80~

Subtask 2 [65%]

No additional constraints.

Input Specification

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

The next ~M~ lines will contain ~3~ integers ~x~, ~y~, and ~z~.

Output Specification

Output one integer, the maximum safety value of a coordinate in space.

Sample Input 1

3 2
1 1 1
2 3 2

Sample Output 1

8

Sample Input 2

12346583 5
1 5 2345
1234 634 1234
999 999 999
12340000 12341230 12340000
12346583 9238732 12346580

Sample Output 2

114237170