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 Ruby (judge verdict: Wrong Answer)

def solve(as, n, aSum)
  return aSum if n == 1
  l = as.first(n - 1)
  lSum = l.inject(:+)
  r = as.last(n - 1)
  rSum = r.inject(:+)
  bs, bSum = if lSum < rSum then [r, rSum] else [l, lSum] end
  if aSum < bSum
    solve(bs, n - 1, bSum)
  else
    solve(bs, n - 1, aSum)
  end
end

while true
  n = gets.to_i
  break if n == 0

  as = n.times.map { gets.to_i }
  puts solve(as, n, as.inject(:+))
end