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 C# (judge verdict: Accepted)

using System;
using System.Linq;

namespace V0022 {
    public class Program {
        public static void Main(string[] args) {
            while(true) {
                var n = int.Parse(Console.ReadLine());
                if(n == 0) break;

                var dp = new int[n][];
                for(var i = 0; i < n; i++){
                    dp[i] = new int[n];
                    for(var j = 0; j < n; j++) {
                        dp[i][j] = int.MinValue;
                    }
                }

                for(var i = 0; i < n; i++) {
                    dp[0][i] = int.Parse(Console.ReadLine());
                }

                for(var i = 1; i < n; i++) {
                    dp[1][i] = dp[0][i - 1] + dp[0][i];
                }

                for(var i = 2; i <= n; i++) {
                    for(var j = i; j < n; j++) {
                        dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j] - dp[i - 2][j - 1];
                    }
                }

                Console.WriteLine(dp.Max(a => a.Max()));
            }
        }
    }
}