#include <bits/stdc++.h>
#define re register
#define LL long long
#define SIZE 1005
using namespace std;
int n;
struct Node
{
	LL w,s,v;
}bl[SIZE];
LL dp[20005],ans=0;
inline bool cmp(Node x,Node y)
{
	return x.w+x.s<y.w+y.s;
}
int main()
{
	cin>>n;
	for(re int i=1;i<=n;++i)
		cin>>bl[i].w>>bl[i].s>>bl[i].v;
	sort(bl+1,bl+n+1,cmp);
	for(re int i=1;i<=n;++i)
		for(re int j=20001;j>=bl[i].w;--j)
			if(bl[i].s+bl[i].w>=j)
				dp[j]=max(dp[j],dp[j-bl[i].w]+bl[i].v),ans=max(ans,dp[j]);	
	cout<<ans<<endl;
	return 0;
} 
### Prompt

Your task is to create 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>
#define re register
#define LL long long
#define SIZE 1005
using namespace std;
int n;
struct Node
{
	LL w,s,v;
}bl[SIZE];
LL dp[20005],ans=0;
inline bool cmp(Node x,Node y)
{
	return x.w+x.s<y.w+y.s;
}
int main()
{
	cin>>n;
	for(re int i=1;i<=n;++i)
		cin>>bl[i].w>>bl[i].s>>bl[i].v;
	sort(bl+1,bl+n+1,cmp);
	for(re int i=1;i<=n;++i)
		for(re int j=20001;j>=bl[i].w;--j)
			if(bl[i].s+bl[i].w>=j)
				dp[j]=max(dp[j],dp[j-bl[i].w]+bl[i].v),ans=max(ans,dp[j]);	
	cout<<ans<<endl;
	return 0;
} 
```