One of the secret chambers in Hogwarts is full of philosopher’s stones. The floor of the chamber is covered by h × w square tiles, where there are h rows of tiles from front (first row) to back (last row) and w columns of tiles from left to right. Each tile has 1 to 100 stones on it. Harry has to grab as many philosopher’s stones as possible, subject to the following restrictions:

• He starts by choosing any tile in the first row, and collects the philosopher’s stones on that tile. Then, he moves to a tile in the next row, collects the philosopher’s stones on the tile, and so on until he reaches the last row.
• When he moves from one tile to a tile in the next row, he can only move to the tile just below it or diagonally to the left or right.

Given the values of h and w, and the number of philosopher’s stones on each tile, write a program to compute the maximum possible number of philosopher’s stones Harry can grab in one single trip from the first row to the last row.

Input

The first line consists of a single integer T, the number of test cases. In each of the test cases, the first line has two integers. The first integer h (1 <= h <= 100) is the number of rows of tiles on the floor. The second integer w (1 <= w <= 100) is the number of columns of tiles on the floor. Next, there are h lines of inputs. The i-th line of these, specifies the number of philosopher’s stones in each tile of the i-th row from the front. Each line has w integers, where each integer m (0 <= m <= 100) is the number of philosopher’s stones on that tile. The integers are separated by a space character.

Output

The output should consist of T lines, (1 <= T <= 100), one for each test case. Each line consists of a single integer, which is the maximum possible number of philosopher’s stones Harry can grab, in one single trip from the first row to the last row for the corresponding test case.

Example

Input:
1
6 5
3 1 7 4 2
2 1 3 1 1
1 2 2 1 8
2 2 1 5 3
2 1 4 4 4
5 2 7 5 1

Output:
32 	

//7+1+8+5+4+7=32

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	tyler_durden: 2015-01-07 08:36:41 first dp :)
	KAI: 2014-12-31 09:58:07 top down TLE. Accepted with bottom up :)
	Ankur Singh: 2014-12-28 15:38:11 why c++4.3.2 is not allowed!
	numerix: 2014-11-05 18:49:36 @Miguel Boland: There are some (few) AC Python solutions and Python works well for that problem. BUT: The data is not formatted correctly, so you cannot read it line by line. Last edit: 2014-11-05 18:54:56
	Miguel Boland: 2014-11-05 17:30:51 Python doesn't work here.... don't even try it
	Fionsel: 2014-11-04 16:48:48 The input description clearly states: "The ith line of these, specifies the number of philosopher’s stones in each tile of the ith row from the front. Each line has w integers" However, a simple test shows that there are not always w integers in every line. Are the last empty tiles on any row expected to have 0 stones, or will it not be possible to visit those tiles? Edit: scrolled to last page to find that the input file does contain enough integers, just not as neatly distributed over the lines as stated in the description. Just thought to mention it such that not everyone with the same problem has to scroll back through all comments. Last edit: 2014-11-04 17:05:58
	ankur shukla: 2014-11-02 16:52:08 Easy One !! Bad Input Format
	amarveer: 2014-10-27 18:32:03 My first dp :)
	jetpack: 2014-10-16 21:21:10 first dp.^_^
	manu4rhyme: 2014-09-22 19:10:12 easy dp..Accepted in one go :)