Mirko has a chessboard with $N$ rows and just three columns. Slavica has written an integer on each field. Mirko has $K$ dominoes at his disposal, their dimensions being $2 \times 1$, and has to arrange all of them on the board without overlapping, in a way that each domino covers exactly two fields of the board. He can rotate the dominoes as he please

Help Mirko cover the largest sum of numbers possible with the dominoes!

-----Input-----
The first line of input contains the integer $N$ ($1 \le N \le 1000$), the number of rows, and $K$ ($1 \le K \le 1000$), the number of dominoes available.

Each of the following $N$ lines contains three integers written in the $i$’th row of the board. All numbers will be less than $10^6$ in absolute value.

-----Output-----
The first and only line of output must contain the maximal sum possible to cover with exactly $K$ dominoes.

-----Examples-----
Sample Input:
5 3
2 1 -1
1 3 2
0 2 3
2 1 1
3 3 0
Sample Output:
16

Source: kattis | Difficulty: HARD


Solutions: