Problem:
Maximum Sum Sequence

Given a sequence of numbers a1, a2, a3, ..., an, find the maximum sum of a contiguous subsequence of those numbers. Note that, a subsequence of one element is also a contiquous subsequence.

Input

The input consists of multiple datasets. Each data set consists of:

n
a1
a2
.
.
an

You can assume that 1 ≤ n ≤ 5000 and -100000 ≤ ai ≤ 100000.

The input end with a line consisting of a single 0.

Output

For each dataset, print the maximum sum in a line.

Sample Input

7
-5
-1
6
4
9
-6
-7
13
1
2
3
2
-2
-1
1
2
3
2
1
-2
1
3
1000
-200
201
0

Output for the Sample Input

19
14
1001

Solution in Haskell (judge verdict: Wrong Answer)

import Data.List
main = interact $ unlines . map (show . maximum_sum_seq) . groupProb . map read . lines

groupProb [] = []
groupProb (0:_) = []
groupProb (n:ns) = (take n ns) : groupProb (drop n ns)

maximum_sum_seq ns = maximum $ map (\xs -> maximum xs - head xs) $ init $ tails ns'
 where ns' = scanl (+) 0 ns