#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; ++i)
#define all(a) (a).begin(), (a).end()

int N;

struct Block {
  int w, s, v;
};

vector<Block> B;

int main() {
  cin >> N;
  B.resize(N);
  int S = 0;
  rep(i, N) {
    cin >> B[i].w >> B[i].s >> B[i].v;
    S = max(S, B[i].s + B[i].w);
  }

  sort(B.rbegin(), B.rend(),
       [&](const Block& a, const Block& b) { return a.s + a.w < b.s + b.w; });

  vector<ll> dp(S + 1, 0);

  rep(i, N) rep(j, S + 1) {
    if (j + B[i].w <= S && B[i].s >= j)
      dp[j] = max(dp[j], dp[j + B[i].w] + B[i].v);
  }

  cout << dp[0] << endl;

  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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.

Examples

Input

3
2 2 20
2 1 30
3 1 40


Output

50


Input

4
1 2 10
3 1 10
2 4 10
1 6 10


Output

40


Input

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000


Output

5000000000


Input

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


Output

22

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; ++i)
#define all(a) (a).begin(), (a).end()

int N;

struct Block {
  int w, s, v;
};

vector<Block> B;

int main() {
  cin >> N;
  B.resize(N);
  int S = 0;
  rep(i, N) {
    cin >> B[i].w >> B[i].s >> B[i].v;
    S = max(S, B[i].s + B[i].w);
  }

  sort(B.rbegin(), B.rend(),
       [&](const Block& a, const Block& b) { return a.s + a.w < b.s + b.w; });

  vector<ll> dp(S + 1, 0);

  rep(i, N) rep(j, S + 1) {
    if (j + B[i].w <= S && B[i].s >= j)
      dp[j] = max(dp[j], dp[j + B[i].w] + B[i].v);
  }

  cout << dp[0] << endl;

  return 0;
}

```