#include <bits/stdc++.h>
using namespace std;
typedef struct node
{
	long long w,s,v;
	bool operator < (const struct node & n)const
	{
		return w+s>n.w+n.s;
	}
}NODE,*PNODE;
NODE a[1001];
long long f[20001];
int main()
{
	int n,i,j;
	long long maxx=0;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%lld%lld%lld",&a[i].w,&a[i].s,&a[i].v);
	sort(a+1,a+1+n);
	for(i=n;i>=1;i--)
	{
		maxx=max(maxx,a[i].v+f[a[i].s]);
		for(j=20001;j>=a[i].w;j--)
				f[j]=max(f[j],f[min(a[i].s,j-a[i].w)]+a[i].v);
	}
	printf("%lld",maxx);
	return 0;
} 
### Prompt

Construct a Cpp code solution to the problem outlined:

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;
typedef struct node
{
	long long w,s,v;
	bool operator < (const struct node & n)const
	{
		return w+s>n.w+n.s;
	}
}NODE,*PNODE;
NODE a[1001];
long long f[20001];
int main()
{
	int n,i,j;
	long long maxx=0;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%lld%lld%lld",&a[i].w,&a[i].s,&a[i].v);
	sort(a+1,a+1+n);
	for(i=n;i>=1;i--)
	{
		maxx=max(maxx,a[i].v+f[a[i].s]);
		for(j=20001;j>=a[i].w;j--)
				f[j]=max(f[j],f[min(a[i].s,j-a[i].w)]+a[i].v);
	}
	printf("%lld",maxx);
	return 0;
} 
```