#include<bits/stdc++.h>
using namespace std;

int n;
long long dp[65536];
struct wd{
	long long w,s,v;
	bool operator < (const wd a) const{
		return w+s<a.w+a.s;
	}
}zhr[1024];

int main(){
	cin>>n;
	for(int i=0;i!=n;++i){
		cin>>zhr[i].w>>zhr[i].s>>zhr[i].v;
	}
	sort(zhr,zhr+n);
	for(int i=0;i<n;++i){
		for(int j=zhr[i].s;j>=0;--j){
			dp[j+zhr[i].w]=max(dp[j+zhr[i].w],dp[j]+zhr[i].v);
		}
	}
	long long ans=0;
	for(int i=0;i<=30000;++i) ans=max(ans,dp[i]);
	cout<<ans<<"\n";
	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;

int n;
long long dp[65536];
struct wd{
	long long w,s,v;
	bool operator < (const wd a) const{
		return w+s<a.w+a.s;
	}
}zhr[1024];

int main(){
	cin>>n;
	for(int i=0;i!=n;++i){
		cin>>zhr[i].w>>zhr[i].s>>zhr[i].v;
	}
	sort(zhr,zhr+n);
	for(int i=0;i<n;++i){
		for(int j=zhr[i].s;j>=0;--j){
			dp[j+zhr[i].w]=max(dp[j+zhr[i].w],dp[j]+zhr[i].v);
		}
	}
	long long ans=0;
	for(int i=0;i<=30000;++i) ans=max(ans,dp[i]);
	cout<<ans<<"\n";
	return 0;
} 
```