#include <bits/stdc++.h>
#define maxs 30005
using namespace std;

struct data {
  long long w, s, v;
};
bool operator<(const data &l, const data &r) {
  return l.s + l.w < r.s + r.w;
}

long long n;
vector<data> v;
long long dp[1005][31000] = {0};

long long solve();

int main() {
  cin >> n;
  v.resize(n);
  for(int i = 0; i < n; ++i)
    cin >> v[i].w >> v[i].s >> v[i].v;
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long ans = 0;
  sort(v.begin(), v.end());
  for(int i = 0; i < n; ++i)
    for(int j = 0; j < maxs; ++j) {
      dp[i + 1][j] = dp[i][j];
      if(j >= v[i].w && j - v[i].w <= v[i].s)
        dp[i + 1][j] =
            max(dp[i + 1][j], dp[i][j - v[i].w] + v[i].v);
      ans = max(ans, dp[i + 1][j]);
    }
  return ans;
}
### Prompt

Generate a Cpp solution to 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>
#define maxs 30005
using namespace std;

struct data {
  long long w, s, v;
};
bool operator<(const data &l, const data &r) {
  return l.s + l.w < r.s + r.w;
}

long long n;
vector<data> v;
long long dp[1005][31000] = {0};

long long solve();

int main() {
  cin >> n;
  v.resize(n);
  for(int i = 0; i < n; ++i)
    cin >> v[i].w >> v[i].s >> v[i].v;
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long ans = 0;
  sort(v.begin(), v.end());
  for(int i = 0; i < n; ++i)
    for(int j = 0; j < maxs; ++j) {
      dp[i + 1][j] = dp[i][j];
      if(j >= v[i].w && j - v[i].w <= v[i].s)
        dp[i + 1][j] =
            max(dp[i + 1][j], dp[i][j - v[i].w] + v[i].v);
      ans = max(ans, dp[i + 1][j]);
    }
  return ans;
}
```