BYTESM2  Philosophers Stone
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.
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 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, 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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Karan Desai:
20150115 07:46:22
easy dp, and the first one, my concept for dp got cleared after solving this, must try dp, and one advice for newbies, think as if dp is nothing and apply proper logic, on solving, u will automatically know how dp works :) 

tyler_durden:
20150107 08:36:41
first dp :) 

KAI:
20141231 09:58:07
top down TLE. Accepted with bottom up :) 

Ankur Singh:
20141228 15:38:11
why c++4.3.2 is not allowed! 

numerix:
20141105 18:49:36
@Miguel Boland: There are some (few) AC Python solutions and Python works well for that problem.


Miguel Boland:
20141105 17:30:51
Python doesn't work here.... don't even try it 

Fionsel:
20141104 16:48:48
The input description clearly states:


ankur shukla:
20141102 16:52:08
Easy One !! Bad Input Format 

amarveer:
20141027 18:32:03
My first dp :)


jetpack:
20141016 21:21:10
first dp.^_^ 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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