Problem Statement

You and Enjapma decided to play a game together, just the $2$ of you.
The rules of the game are as follows.

• $1$ . There are $N$ treasure chests on a desk. $N$ is even. Initially, all treasure chests are closed.
• $2$ . Each treasure chest contains some gems. There are $M$ types of gems, and the $i$-th treasure chest contains $A_{ij}$ gems of the $j$-th type.
• $3$ . The game is played with a first player and a second player. You are the first player, and Enjapma is the second player.
• $4$ . The first and second players take turns choosing $1$ closed treasure chest, opening it, and obtaining all the gems inside. This is repeated until there are no closed treasure chests left.
• $5$ . Each player's score, where $C_j$ is the number of gems of the $j$-th type that player has obtained, is given by ${C_1}^2 + {C_2}^2 + {C_3}^2 + ... + {C_M}^2$.

Input

$N\ M$
$A_{11}\ A_{12}\ \dots\ A_{1M}$
$A_{21}\ A_{22}\ \dots\ A_{2M}$
$\vdots$
$A_{N1}\ A_{N2}\ \dots\ A_{NM}$

• All inputs are integers.
• $N$ is even.
• $2 \le N \le 300$
• $1 \le M \le 300$
• $0 \le A_{ij} \le 100$

Output

Output the value of $X-Y$ when you use a strategy to maximize the value of $X - Y$ and Enjapma uses a strategy to minimize the value of $X-Y$.
Print a newline at the end.

Sample

4 3
1 2 0
2 0 1
1 1 0
0 0 1

5

2 4
2 0 2 0
0 5 2 2

25

4 3
0 0 0
0 0 0
0 0 0
0 0 0

0