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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timmyx:
20220111 15:42:17
not possible with python because of nzec error.


surfeyone:
20211217 04:53:28
this is a nice confidence booster 

luisalfredo92:
20211128 05:09:37
Test cases are wrong: they're not separated by line jump ("\n") but always by spaces (" ") so if you're doing this on C# or Java... it simply won't work 

aniket_2109:
20210304 06:44:36
hint1: use dp.


pro_shubham_7:
20210127 16:50:58
Why isn't there option for Python 3 users ? 

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 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  ADA95 ASM32 BASH BF C CSHARP CPP C99 CLPS LISP clisp LISP sbcl D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PASGPC PASFPC PERL PHP PIKE PRLGswi PYTHON RUBY SCM guile SCM qobi ST TEXT WHITESPACE 