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(input)
  ss = input.split("\n")

  nss = []
  while true
    n = ss.shift.to_i
    break if n == 0

    ns = []
    n.times{ns.push(ss.shift.to_i)}
    nss.push(ns)
  end

  a = []
  nss.each do |ns|
    b = []
    b[0] = nil
    ns.each_with_index do |n, i|
      b[i+1] = [n, n]
      1.upto(i) do |k|
        b[k] = [b[k][0]+n, [b[k][0]+n, b[k][1]].max]
      end
    end
    max = 0
    1.upto(b.size-1) do |i|
      max = b[i][1] if max < b[i][1]
    end
    a.push(max)
  end
  a
end

solve(gets(nil)).each {|a| puts a}