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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;

public class Main {

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }

        public double nextDouble() {
            return Float.parseFloat(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

    static InputReader sc;
    static PrintWriter pw;
    
    static int max;


    public static void main(String[] args) throws Exception {
        sc = new InputReader(System.in);
        pw = new PrintWriter(System.out);

        int n = sc.nextInt();

        Block[] blocks = new Block[n];

        for (int i = 0; i < n; i++) {
            blocks[i] = new Block(sc.nextInt(), sc.nextInt(), sc.nextInt());
        }

        Arrays.sort(blocks);
        
        max = 1000000;

        long[] dp = new long[max];

        for (Block block: blocks) {
            for (int i = Math.min(max - block.weight, block.solidness); i >= 0; i--) {
                dp[i + block.weight] = Math.max(dp[i + block.weight], dp[i] + block.value);
            }
        }

        long result = 0;

        for (int i = 0; i <= max; i++) {
            result = Math.max(result, dp[i]);
        }

        pw.println(result);

        pw.close();
    }

    static class Block implements Comparable<Block> {
        int weight, solidness, value;

        Block(int weight , int solidness, int value) {
            this.weight = weight;
            this.solidness = solidness;
            this.value = value;
        }

        @Override
        public int compareTo(Block o) {
            return (this.weight + this.solidness) - (o.weight + o.solidness);
        }
    }
}