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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

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

    Arrays.sort(blocks, Comparator.comparingInt(b -> b.s + b.w));

    final int MAX_W = 1000_000;
    long[] dp = new long[MAX_W + 1];
    for (int i = 1; i <= N; i++) {
      Block b = blocks[i - 1];
      for (int j = b.s; j >= 0; j--) {
        dp[j + b.w] = Math.max(dp[j] + b.v, dp[j + b.w]);
      }
    }

    long max = 0;
    for (int i = 0; i <= MAX_W; i++) {
      max = Math.max(max, dp[i]);
    }
    System.out.println(max);
  }

  private static class Block {
    public final int w;
    public final int s;
    public final int v;

    private Block(int w, int s, int v) {
      this.w = w;
      this.s = s;
      this.v = v;
    }
  }
}