B. Numbers Box
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

You are given a rectangular grid with $$$n$$$ rows and $$$m$$$ columns. The cell located on the $$$i$$$-th row from the top and the $$$j$$$-th column from the left has a value $$$a_{ij}$$$ written in it.

You can perform the following operation any number of times (possibly zero):

  • Choose any two adjacent cells and multiply the values in them by $$$-1$$$. Two cells are called adjacent if they share a side.

Note that you can use a cell more than once in different operations.

You are interested in $$$X$$$, the sum of all the numbers in the grid.

What is the maximum $$$X$$$ you can achieve with these operations?


Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). Description of the test cases follows.

The first line of each test case contains two integers $$$n$$$,$$$m$$$ ($$$2 \le n$$$, $$$m \le 10$$$).

The following $$$n$$$ lines contain $$$m$$$ integers each, the $$$j$$$-th element in the $$$i$$$-th line is $$$a_{ij}$$$ ($$$-100\leq a_{ij}\le 100$$$).


For each testcase, print one integer $$$X$$$, the maximum possible sum of all the values in the grid after applying the operation as many times as you want.

2 2
-1 1
1 1
3 4
0 -1 -2 -3
-1 -2 -3 -4
-2 -3 -4 -5

In the first test case, there will always be at least one $$$-1$$$, so the answer is $$$2$$$.

In the second test case, we can use the operation six times to elements adjacent horizontally and get all numbers to be non-negative. So the answer is: $$$2\times 1 + 3\times2 + 3\times 3 + 2\times 4 + 1\times 5 = 30$$$.