#include <bits/stdc++.h>
#define ll long long
using namespace std;
struct node
{
	ll s,w,v;
};
node bl[1010];
ll n,f[20010],ans;
bool cmp(node a1,node b1)
{
	return a1.s+a1.w<b1.s+b1.w;
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>bl[i].w>>bl[i].s>>bl[i].v;
	sort(bl+1,bl+n+1,cmp);
	for(int i=1;i<=n;i++)
	{
		for(int j=20010;j>=bl[i].w;j--)
		{
			if(bl[i].s+bl[i].w>=j)
				f[j]=max(f[j],f[j-bl[i].w]+bl[i].v);
			ans=max(ans,f[j]);
		}
	}
	cout<<ans<<endl;
	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>
#define ll long long
using namespace std;
struct node
{
	ll s,w,v;
};
node bl[1010];
ll n,f[20010],ans;
bool cmp(node a1,node b1)
{
	return a1.s+a1.w<b1.s+b1.w;
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>bl[i].w>>bl[i].s>>bl[i].v;
	sort(bl+1,bl+n+1,cmp);
	for(int i=1;i<=n;i++)
	{
		for(int j=20010;j>=bl[i].w;j--)
		{
			if(bl[i].s+bl[i].w>=j)
				f[j]=max(f[j],f[j-bl[i].w]+bl[i].v);
			ans=max(ans,f[j]);
		}
	}
	cout<<ans<<endl;
	return 0;
}
```