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: Time Limit Exceeded)

# coding: utf-8

class MaxSumSeq
  def solve
    loop do
      n = gets.chomp.to_i
      break if n == 0

      candidates = []
      array = read(n)
      len = array.length
      (0..len-1).each do |i|
        (i..len-1).each do |j|
          sum = 0
          (i..j).each do |k|
            sum += array[k]
          end
          candidates << sum
        end
      end
      max = find_max(candidates)
      puts max
    end
  end

  def find_max(array)
    max = nil
    array.each do |i|
      if max == nil || max < i then
        max = i
      end
    end
    max
  end

  def read(n)
    array = []
    previous = 0
    current = 0
    n.times do |i|
      current = gets.chomp.to_i

      if previous == 0 ||
        (previous < 0 && current < 0) ||
        (previous > 0 && current > 0) then
        previous += current
      else
        array << previous
        previous = current
      end
      if i == n - 1 then
        array << previous
      end
    end
    array
  end
end

MaxSumSeq.new.solve