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
import Control.Monad

main = do
    n <- readLn
    unless ( n == 0) $ do
        nums <- replicateM n readLn
        print $ mss2 nums
        main

mss1 :: [Int] -> Int
mss1 = maximum.map sum.concatMap inits.tails

mss2 = maximum . scanr (\x y -> 0 `max` (x+y)) 0