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 qualified Data.Vector.Unboxed as V
import Control.Monad

maxSumSeq :: V.Vector Int -> Int
maxSumSeq ns = f sums
    where
        sums = V.scanl' (+) 0 ns
        f ss
            | V.null ss = 0
            | otherwise  = let
                (pre, post) = V.splitAt (V.maxIndex ss) ss
                current = if V.null pre then 0 else V.head post - V.minimum pre
                in
                    max current (f (V.tail post))


main = do
    n <- readLn
    unless (n == 0) $ do
        replicateM n readLn >>= print . maxSumSeq . V.fromList
        main