
#include <cstdio>
#include <vector>
#include <algorithm>

int n;
int W[1000], S[1000], V[1000];


long long int dp[20001];

int main(){
  scanf("%d", &n);
  for(int i = 0; i < n; i++) scanf("%d%d%d", W+i, S+i, V+i);
  std::vector<std::pair<int, int> > v;
  for(int i = 0; i < n; i++){
    v.emplace_back(S[i] + W[i], i);
  }
  std::sort(v.begin(), v.end());
  for(int i = 0; i < n; i++){
    int j = v[i].second;
    for(int k = S[j] + W[j]; k >= W[j]; k--){
      dp[k] = std::max(dp[k], dp[k - W[j]] + V[j]);
    }
  }
  long long int ans = 0;
  for(int i = 0; i <= 20000; i++) ans = std::max(ans, dp[i]);
  printf("%lld\n", ans);
  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 <cstdio>
#include <vector>
#include <algorithm>

int n;
int W[1000], S[1000], V[1000];


long long int dp[20001];

int main(){
  scanf("%d", &n);
  for(int i = 0; i < n; i++) scanf("%d%d%d", W+i, S+i, V+i);
  std::vector<std::pair<int, int> > v;
  for(int i = 0; i < n; i++){
    v.emplace_back(S[i] + W[i], i);
  }
  std::sort(v.begin(), v.end());
  for(int i = 0; i < n; i++){
    int j = v[i].second;
    for(int k = S[j] + W[j]; k >= W[j]; k--){
      dp[k] = std::max(dp[k], dp[k - W[j]] + V[j]);
    }
  }
  long long int ans = 0;
  for(int i = 0; i <= 20000; i++) ans = std::max(ans, dp[i]);
  printf("%lld\n", ans);
  return 0;
}

```