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
hide comments
Timmy Jose:
20151129 20:47:58
My obviously greedy approach did not pass muster beyond the given test case. Clearly I need to learn DP now. Good motivation though! 

munjal:
20151024 19:13:30
gives TLE with memorization technique in java


Gustav:
20151018 13:40:52
************


nietaki:
20151018 03:42:11
The input is malformed  don't waste your time on this problem, or write your solution in a way that doesn't depend on the locations of new lines and space counts.


vijay meena:
20151014 08:45:33
Ac in one go ! easy dp just use bottom up 

Akshay Damle:
20151013 14:33:06
Don't try this in Python. The input format is wrong. 

Abishek:
20150917 12:45:12
wow .. learning the power of dp with problems like these ...awesome one :) 

Vivek:
20150907 21:58:52
Very easy problem.


Surendra :
20150828 11:06:06
can any one give the other test cases pls


anuveshkothari:
20150827 14:44:31
@iammangod96 comment helps 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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