#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
int MAX = 2e4;

int main(){
  int n;
  cin >> n;
  int w[n], s[n]; ll v[n];
  rep(i,n) cin >> w[i] >> s[i] >> v[i];
  int ord[n];
  rep(i,n) ord[i] = i;
  sort(ord,ord+n,[&](int a, int b){return w[a]+s[a] < w[b]+s[b];});
  vector<vector<ll>> dp(n+1,vector<ll>(MAX));
  rep(i,n) {
    rep(j,MAX) {
      dp[i+1][j] = max(dp[i+1][j],dp[i][j]);
      if(s[ord[i]] >= j) {
        int wa = min(MAX-1,j+w[ord[i]]);
        dp[i+1][wa] = max(dp[i+1][wa],dp[i][j]+v[ord[i]]);
      }
    }
  }
  ll ans = 0;
  rep(i,MAX) ans = max(ans,dp[n][i]);
  cout << ans << endl;
  return 0;
}
### Prompt

Please create a solution in CPP 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>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
int MAX = 2e4;

int main(){
  int n;
  cin >> n;
  int w[n], s[n]; ll v[n];
  rep(i,n) cin >> w[i] >> s[i] >> v[i];
  int ord[n];
  rep(i,n) ord[i] = i;
  sort(ord,ord+n,[&](int a, int b){return w[a]+s[a] < w[b]+s[b];});
  vector<vector<ll>> dp(n+1,vector<ll>(MAX));
  rep(i,n) {
    rep(j,MAX) {
      dp[i+1][j] = max(dp[i+1][j],dp[i][j]);
      if(s[ord[i]] >= j) {
        int wa = min(MAX-1,j+w[ord[i]]);
        dp[i+1][wa] = max(dp[i+1][wa],dp[i][j]+v[ord[i]]);
      }
    }
  }
  ll ans = 0;
  rep(i,MAX) ans = max(ans,dp[n][i]);
  cout << ans << endl;
  return 0;
}
```