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)

main = getContents >>= mapM_ (print . maximum_sum_seq) . reverse . fin [] . map read . init . lines
fin acc [] = acc
fin acc (n:ns) = fin ((take (fromIntegral n) ns):acc) (drop (fromIntegral n) ns)
maximum_sum_seq ns = max (maximum frombot - minimum frombot) (maximum ns')
 where
  ns' = scanl (+) 0 ns
  frombot = dropWhile (/= minimum ns') ns'