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

#define pb push_back
#define fi first
#define se second
#define ll long long
#define pq priority_queue
#define mp make_pair
#define pii pair<int,int>
#define mod 998244353

int lowbit(int x) {return x&(-x);}

int n;
struct node{
	int s,w,v;
}a[1010];

ll f[30010];

bool com(node a,node b) {
	return -a.w+b.w>-b.s+a.s;
} 

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d%d%d",&a[i].w,&a[i].s,&a[i].v);
	sort(a+1,a+n+1,com);
	ll ans=0ll;
	for (int i=1;i<=n;i++)
		for (int j=a[i].s;j>=0;j--) {
			f[j+a[i].w]=max(f[j+a[i].w],f[j]+(ll)a[i].v);
			ans=max(ans,f[j+a[i].w]);
		}
	cout<<ans;
	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;

#define pb push_back
#define fi first
#define se second
#define ll long long
#define pq priority_queue
#define mp make_pair
#define pii pair<int,int>
#define mod 998244353

int lowbit(int x) {return x&(-x);}

int n;
struct node{
	int s,w,v;
}a[1010];

ll f[30010];

bool com(node a,node b) {
	return -a.w+b.w>-b.s+a.s;
} 

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d%d%d",&a[i].w,&a[i].s,&a[i].v);
	sort(a+1,a+n+1,com);
	ll ans=0ll;
	for (int i=1;i<=n;i++)
		for (int j=a[i].s;j>=0;j--) {
			f[j+a[i].w]=max(f[j+a[i].w],f[j]+(ll)a[i].v);
			ans=max(ans,f[j+a[i].w]);
		}
	cout<<ans;
	return 0;
}
```