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: Wrong Answer)


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

public class Main {
    static class node implements Comparable<node> {
        int w;
        int s;
        int sum;
        long v;

        public node(int w, int s, long v) {
            this.w = w;
            this.s = s;
            this.v = v;
            sum = w + s;
        }

        @Override
        public int compareTo(node o) {
            if (sum != o.sum) {
                return Integer.compare(sum, o.sum);
            }
            return Integer.compare(o.w, w);
        }
    }


    public static void main(String[] aaaa) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        node[] nodes = new node[10000];
        long[] dp = new long[100005];
        Arrays.fill(dp, -1);
        dp[0] = 0;
        for (int i = 0; i < n; i++) {
            nodes[i] = new node(scanner.nextInt(), scanner.nextInt(), scanner.nextInt());
        }
        Arrays.sort(nodes, 0, n);
        for (int i = 0; i < n; i++) {
            for (int j = nodes[i].s; j >= 0; j--) {
                if (dp[j] >= 0) {

                    if (j + nodes[i].w <= dp.length) {
                        dp[j + nodes[i].w] = Math.max(dp[j + nodes[i].w], dp[j] + nodes[i].v);
                    }
                }
            }



        }
        long max = 0;
        for (int i = 0; i < 1000; i++) {
            //System.out.println(i + " " + dp[i]);
            max = Math.max(max, dp[i]);
        }
        System.out.println(max);



    }
}