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)

while true
  n = gets.to_i
  if n == 0
    break
  end
  a = Array.new(n)
  for i in 0..n-1
    a[i] = gets.to_i
  end
  max = a[0]
  sum = Array.new(n)
  sum[0] = [a[0],1] # sum[i][1] includes a[i] and sum[i][0] does not
  for i in 1..n-1
    if a[i] <= 0
      sum[i] = [sum[i-1][0],0]
    elsif sum[i-1][1] == 1
      sum[i] = [sum[i-1][0]+a[i],1]
    elsif a[i] > sum[i-1][0]
      sum[i] = [a[i],1]
    else
      sum[i] = [sum[i-1][0],0]
    end
    if sum[i][0] > max
      max = sum[i][0]
    end
  end
  puts max
end