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;

public static class Program {
    public static void Main() {
        int n=int.Parse(Console.ReadLine());
        Tuple<int,int,long>[]array=new Tuple<int,int,long>[n];
        int W=0,S=0;
        for(int i=0;i<n;i++){
            int[]wsv=Console.ReadLine().Split().Select(int.Parse).ToArray();
            int w=wsv[0];
            int s=wsv[1];
            long v=wsv[2];
            array[i]=new Tuple<int,int,long>(w+s,s,v);
            Chmax(ref S, s);
            Chmax(ref W, w);
        }
        W+=S;
        Array.Sort(array);

        long[]dp=new long[W+1];
        for(int i=0;i<n;i++){
            int w=array[i].Item1-array[i].Item2;
            int s=array[i].Item2;
            long v=array[i].Item3;
            for(int j=s;j>=0;j--){
                Chmax(ref dp[j+w], dp[j]+v);
            }

            // Console.Write($"[w s v] {w} {s} {v}:");
            // for(int j=0;j<=W;j++){
            //     Console.Write($" {dp[j]}");
            // }
            // Console.Write("\n");
        }
        long ans=0;
        for(int i=0;i<=W;i++){
            Chmax(ref ans, dp[i]);
        }
        Console.WriteLine(ans);
    }

    public static void Chmax(ref int x, int y){
        x = Math.Max(x,y);
    }
    public static void Chmax(ref long x, long y){
        x = Math.Max(x,y);
    }
}