#include <bits/stdc++.h>

using namespace std;

using ll = long long;

struct S {
  int w, s, v;
  inline void read () {
    cin >> w >> s >> v;
  }
  bool operator <(const S& b) const {
    return w + s < b.w + b.s;
  }
};

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n;
  cin >> n;
  vector < S > in(n);
  int MAX_S = 20002;
  for (int i = 0; i < n; ++i)
    in[i].read();
  sort (in.begin(), in.end());
  vector < ll > dp (MAX_S + 1);
  for (S block : in)
    for (int w = min (block.s, MAX_S - block.w); w >= 0; --w)
      dp[w + block.w] = max (dp[w + block.w], dp[w] + block.v);
  ll answer = 0;
  for (int i = 0; i <= MAX_S; ++i)
    answer = max (answer, dp[i]);
  cout << answer;
}

### Prompt

In CPP, your task is to solve the following problem:

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;

using ll = long long;

struct S {
  int w, s, v;
  inline void read () {
    cin >> w >> s >> v;
  }
  bool operator <(const S& b) const {
    return w + s < b.w + b.s;
  }
};

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n;
  cin >> n;
  vector < S > in(n);
  int MAX_S = 20002;
  for (int i = 0; i < n; ++i)
    in[i].read();
  sort (in.begin(), in.end());
  vector < ll > dp (MAX_S + 1);
  for (S block : in)
    for (int w = min (block.s, MAX_S - block.w); w >= 0; --w)
      dp[w + block.w] = max (dp[w + block.w], dp[w] + block.v);
  ll answer = 0;
  for (int i = 0; i <= MAX_S; ++i)
    answer = max (answer, dp[i]);
  cout << answer;
}

```