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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

using i64 = int64_t;

int main() {
#ifdef GOLIKOV
  freopen("in", "rt", stdin);
#endif
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int n;
  cin >> n;

  struct item {
    int w, s, v;
  };
  vector<item> a(n);
  for (auto& x : a) {
    cin >> x.w >> x.s >> x.v;
  }

  sort(a.begin(), a.end(), [](auto& x, auto& y) {
    return x.w + x.s < y.w + y.s;
  });
  int const W = (int) 2e4 + 20;

  vector<i64> answer(W + 1);
  for (auto& x : a) {
    for (int w = min(x.s, W - x.w); w >= 0; --w) {
      answer[w + x.w] = max(answer[w + x.w], answer[w] + x.v);
    }
  }
  cout << (*max_element(answer.begin(), answer.end())) << '\n';
  return 0;
}