Problem:
Score : 100 points

Problem Statement

There are N blocks, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.

Taro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order.
Here, the tower must satisfy the following condition:

For each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.

Find the maximum possible sum of the values of the blocks contained in the tower.

Constraints

All values in input are integers.

1 \leq N \leq 10^3

1 \leq w_i, s_i \leq 10^4

1 \leq v_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
w_1 s_1 v_1
w_2 s_2 v_2
:
w_N s_N v_N

Output

Print the maximum possible sum of the values of the blocks contained in the tower.

Sample Input 1

3
2 2 20
2 1 30
3 1 40

Sample Output 1

50

If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.

Sample Input 2

4
1 2 10
3 1 10
2 4 10
1 6 10

Sample Output 2

40

Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.

Sample Input 3

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

8
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5

Sample Output 4

22

We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static readonly long Mod = 1000000000 + 7;

        static void Main(string[] args)
        {
            var N = Sarray()[0];
            var wst = new Tuple<long,long,long,long>[N];
            for (var i = 0; i < N; ++i)
            {
                var t = Sarray();
                wst[i] = new Tuple<long,long,long, long>(t[0] + t[1], t[0], t[1], t[2]);//w+s,w,s,v
            }
            Array.Sort<Tuple<long, long, long, long>>(wst, (l, r) => (int)(l.Item1 - r.Item1));
            var len = wst[N - 1].Item2 + wst[N - 1].Item3;
            var dp = new long[len + 1].Select(_ => -1L).ToArray();
            dp[0] = 0;
            for (var i = 0; i < N; ++i)
            {
                for (var j = wst[i].Item3; 0 <= j; --j)
                    if (dp[j] != -1)
                        dp[j + wst[i].Item2] = Max(dp[j + wst[i].Item2], dp[j] + wst[i].Item4);
            }
            WriteLine(dp.Max());
        }
    }
}