#include<bits/stdc++.h>
using namespace std;
#define nn 1008
#define ll long long
#define pii pair<int,int>
int n;ll w[nn],s[nn],v[nn],f[20008],id[nn];
bool cmp(int x,int y)
{
	return s[x]+w[x]>s[y]+w[y];
}
ll ans=0;
void upd(ll &x,ll y)
{
	ans=max(ans,y);
	x=max(x,y);
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++) cin>>w[i]>>s[i]>>v[i],id[i]=i;
	sort(id+1,id+n+1,cmp);
	for(int di=1;di<=n;di++)
	{
		int i=id[di];
		for(int j=0;j<20004;j++)
		{
			if(j>=w[i])
				upd(f[min(j-w[i],s[i])],f[j]+v[i]);
		}
	}
	cout<<ans;
    return 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<bits/stdc++.h>
using namespace std;
#define nn 1008
#define ll long long
#define pii pair<int,int>
int n;ll w[nn],s[nn],v[nn],f[20008],id[nn];
bool cmp(int x,int y)
{
	return s[x]+w[x]>s[y]+w[y];
}
ll ans=0;
void upd(ll &x,ll y)
{
	ans=max(ans,y);
	x=max(x,y);
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++) cin>>w[i]>>s[i]>>v[i],id[i]=i;
	sort(id+1,id+n+1,cmp);
	for(int di=1;di<=n;di++)
	{
		int i=id[di];
		for(int j=0;j<20004;j++)
		{
			if(j>=w[i])
				upd(f[min(j-w[i],s[i])],f[j]+v[i]);
		}
	}
	cout<<ans;
    return 0;
}
```