#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

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

int main(){
  int n,maxwt=0;
  cin>>n;
  vector<block> v(n);
  for(int i=0;i<n;i++)
  {
  	cin>>v[i].w>>v[i].s>>v[i].v;
    maxwt+=v[i].w;
  }
  sort(v.begin(),v.end());
  vector<long> dp(maxwt+5);
  for(int i=0;i<n;i++)
  {
	for(int j=min(v[i].s,maxwt-v[i].w);j>=0;j--)
      dp[j+v[i].w]=max(dp[j+v[i].w],dp[j]+v[i].v);
  }
  long ans=-1;
  for(int j=maxwt;j>=0;j--)
    ans=max(ans,dp[j]);
  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<iostream>
#include<vector>
#include<algorithm>
using namespace std;

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

int main(){
  int n,maxwt=0;
  cin>>n;
  vector<block> v(n);
  for(int i=0;i<n;i++)
  {
  	cin>>v[i].w>>v[i].s>>v[i].v;
    maxwt+=v[i].w;
  }
  sort(v.begin(),v.end());
  vector<long> dp(maxwt+5);
  for(int i=0;i<n;i++)
  {
	for(int j=min(v[i].s,maxwt-v[i].w);j>=0;j--)
      dp[j+v[i].w]=max(dp[j+v[i].w],dp[j]+v[i].v);
  }
  long ans=-1;
  for(int j=maxwt;j>=0;j--)
    ans=max(ans,dp[j]);
  cout<<ans;
  
}
```