ROCK  Sweet and Sour Rock
A manufacturer of sweets has started production of a new type of sweet called rock. Rock comes in sticks composed of onecentimetrelong segments, some of which are sweet, and the rest are sour. Before sale, the rock is broken up into smaller pieces by splitting it at the connections of some segments.
Today's children are very particular about what they eat, and they will only buy a piece of rock if it contains more sweet segments than sour ones. Try to determine the total length of rock which can be sold after breaking up the rock in the best possible way.
Input
The input begins with the integer t, the number of test cases. Then t test cases follow.
For each test case, the first line of input contains one integer N  the length of the stick in centimetres (1<=N<=200). The next line is a sequence of N characters '0' or '1', describing the segments of the stick from the left end to the right end ('0' denotes a sour segment, '1'  a sweet one).
Output
For each test case output a line with a single integer: the total length of rock that can be sold after breaking up the rock in the best possible way.
Example
Sample input: 2 15 100110001010001 16 0010111101100000 Sample output: 9 13
hide comments
your_mom123:
20210320 10:53:38
mhmmm Last edit: 20210320 10:53:54 

nitesh_007:
20200715 18:51:40
Last edit: 20200715 18:58:49 

ks1999:
20200423 19:42:30
Can be solved in O(n^2), i don't know about O(n) solution. Cool question, even cooler solution. 

an09mous:
20200406 16:47:27
Very beautiful problem if you figure out how to do it in O(n^2) 

cpp219:
20200201 11:22:11
my 100th submission :)))


chodermal:
20191120 17:00:48
is there O(n) solution to this problem? 

shubham97361:
20190609 22:10:46
Good problem. 

anshumanc007:
20181219 11:01:19
can be solved in { time>0 (n^3) space >0(n^2) } as well as { time> 0(n^2) space>0(n) }. 

a161112225:
20180905 20:24:22
why i am getting WA and in which test case ? i am trying with partition DP (iterative ) 

aman_sachin200:
20180614 00:10:48
Awesome One!! 
Added by:  adrian 
Date:  20040803 
Time limit:  7s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  based on a problem from the VII Polish Collegiate Team Programming Contest (AMPPZ), 2002 