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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s6j4_10:
20160215 13:24:22
Nice DP problem :)


ajaysingh:
20160206 18:17:35
My first DP problem :) 

Aqib Ahmed J:
20160129 18:40:54
AC in one go :) My 3rd DP problem :) Loving it ! 

Rajat Jain:
20160127 19:43:34
ac in 1 go... good prob for beginners. :) 

try2catch:
20160123 12:41:33
A chyuttzssspaah problem....java code giving TLE


gibibyte:
20160116 04:56:14
thanks a lot guys. solved it after reading several helpful comments 

nitin jain:
20160113 18:13:42
simple DP :) 

dwij28:
20160110 17:17:28
Nice.. Must for beginners in DP.. 

dokz:
20160106 09:44:31
Completed in C#, got NZEC runtime error :( 

karthik1997:
20151229 17:44:26
Dp . Best one for beginners though . For Similar approach  @http://www.geeksforgeeks.org/dynamicprogrammingset6mincostpath/

Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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