#include<bits/stdc++.h>
using namespace std;
#define ll long long int

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

};

int main()
{
    int n;
    cin>>n;
    vector<S> boxes(n);
    int mx_cap=20005;;
    for(int i=0;i<n;i++){
        cin>>boxes[i].w>>boxes[i].s>>boxes[i].v;
        //mx_cap=max(mx_cap,boxes[i].s+boxes[i].w);

    }
    sort(boxes.begin(),boxes.end());
  vector<ll> dp(mx_cap+1,0);

  for(auto box:boxes){
     for(int cap=min(box.s,mx_cap-box.w);cap>=0;--cap){
         dp[cap+box.w]=max(dp[cap+box.w],dp[cap]+box.v);
     }
  }

       ll ans=INT_MIN;
       for(int cap=1;cap<=mx_cap;cap++){
         ans=max(ans,dp[cap]);
       }

    cout<<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>
using namespace std;
#define ll long long int

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

};

int main()
{
    int n;
    cin>>n;
    vector<S> boxes(n);
    int mx_cap=20005;;
    for(int i=0;i<n;i++){
        cin>>boxes[i].w>>boxes[i].s>>boxes[i].v;
        //mx_cap=max(mx_cap,boxes[i].s+boxes[i].w);

    }
    sort(boxes.begin(),boxes.end());
  vector<ll> dp(mx_cap+1,0);

  for(auto box:boxes){
     for(int cap=min(box.s,mx_cap-box.w);cap>=0;--cap){
         dp[cap+box.w]=max(dp[cap+box.w],dp[cap]+box.v);
     }
  }

       ll ans=INT_MIN;
       for(int cap=1;cap<=mx_cap;cap++){
         ans=max(ans,dp[cap]);
       }

    cout<<ans;
}

```