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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it_uchi:
20210107 16:41:55
Simple DP. Messed up with Base Cases and went wrong multiple time. 

sarkybastard:
20201110 20:11:37
nobody caresssssssssssssssssssssssssssss!!!!!!!!!!!!!!!!!!!!!!!!!! 

kxbaphomet_666:
20201107 06:30:06
AC in one goooooooooooo!!!!!!!!!!!!!!!!! 

sarkybastard:
20201104 21:49:19
@kanishkverma_1 perhaps your java code is just buggy, and the same bugs in cpp are ignored 

kanishkverma_1:
20201104 11:24:55
Problem is super messed up for java . AC in one go in cpp but NZEC in java 

saurabh_shinde:
20200912 20:25:03
Nice dp problem.. think each tile as state.. how to arrive at answer at each tile. If you are not getting what I am saying friend, just go and watch dynamic programming video on Youtube channel name "errichto". You will be just fine 

bardend:
20200829 04:06:29


shreedhark:
20200828 19:13:45
AC in one go...... good dp problem!! 

ckanzz:
20200820 12:27:07
Good Dp problem use bottomup 

iamtanishq:
20200819 04:04:59
My second DP problem, I'm lovin it ngl! 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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