#include<iostream>
#include<vector>
#include<algorithm>
#define int long long
using namespace std;
const int N=1e3+2;
const int M=2e4+2;
pair<pair<int,int>,int>  lis[N];
int dp[M];
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k,l;
	cin>>n;
	for(i=1;i<=n;i++){
		cin>>lis[i].first.first>>lis[i].first.second>>lis[i].second;
	}
	sort(lis+1,lis+1+n,[&](pair<pair<int,int>,int> x,pair<pair<int,int>,int> y){
		return x.first.first+x.first.second>y.first.first+y.first.second;
	}); 
	for(i=1;i<=n;i++){
		for(j=lis[i].first.first;j<=lis[i].first.second+lis[i].first.first;j++){
			dp[j-lis[i].first.first]=max(dp[j-lis[i].first.first],dp[j]+lis[i].second);
		}
//		for(j=1;j<=5;j++){
//			cout<<dp[j]<<" ";
//		}
//		cout<<endl;
	}
	cout<<dp[0];
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
#define int long long
using namespace std;
const int N=1e3+2;
const int M=2e4+2;
pair<pair<int,int>,int>  lis[N];
int dp[M];
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k,l;
	cin>>n;
	for(i=1;i<=n;i++){
		cin>>lis[i].first.first>>lis[i].first.second>>lis[i].second;
	}
	sort(lis+1,lis+1+n,[&](pair<pair<int,int>,int> x,pair<pair<int,int>,int> y){
		return x.first.first+x.first.second>y.first.first+y.first.second;
	}); 
	for(i=1;i<=n;i++){
		for(j=lis[i].first.first;j<=lis[i].first.second+lis[i].first.first;j++){
			dp[j-lis[i].first.first]=max(dp[j-lis[i].first.first],dp[j]+lis[i].second);
		}
//		for(j=1;j<=5;j++){
//			cout<<dp[j]<<" ";
//		}
//		cout<<endl;
	}
	cout<<dp[0];
}
```