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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

static class Program
{
    static void Main()
    {
        var q =
            from n in RepeatInfinite<Func<string>>( Console.ReadLine )
                .Select( x => int.Parse( x() ) )
                .TakeWhile( x => x > 0 )
            select Enumerable.Repeat<Func<string>>( Console.ReadLine, n )
                .Select( x => int.Parse( x() ) )
                .SkipWhile( x => x < 0 )
                .Aggregate(
                    new { nneg = true, sum = 0L, sq = new List<long>( n ) },
                    (x, y) => {
                        if ( x.nneg && y >= 0 || !x.nneg && y < 0 )
                            return new { nneg = x.nneg, sum = x.sum + y, sq = x.sq };
                        x.sq.Add( x.sum );
                        return new { nneg = !x.nneg, sum = (long)y, sq = x.sq };
                    },
                    x => {
                        x.sq.Add( x.sum );
                        return x.sq;
                    } )
                .Select( (x, i) => new { v = x, k = ( i + 1 ) >> 1 } )
                .GroupBy( x => x.k, x => x.v )
                .Select( x => x.Sum() )
                .SkipWhile( x => x < 0 )
                .Aggregate(
                    new { sum = 0L, max = 0L },
                    (x, y) => {
                        if ( y < 0 )
                            return new { sum = x.sum + y, max = x.max };
                        var sum = x.sum + y >= 0 ? x.sum + y : y;
                        return new { sum, max = Math.Max( x.max, sum ) };
                    },
                    x => x.max );
        q.ToList().ForEach( Console.WriteLine );
    }

    static IEnumerable<TSource> RepeatInfinite<TSource>(TSource source)
    {
        while ( true )
            yield return source;
    }
}