#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<int,int> pii;
typedef pair<int,pii> box;
#define s first
#define w second.first
#define v second.second
#define maxn 1005
#define maxs 20005
int main()
{
	int n;
	scanf("%d",&n);
	box b[maxn];
	for(int i=0; i<n; i++){
		scanf("%d%d%d", &b[i].w, &b[i].s, &b[i].v);
		b[i].s += b[i].w;
	}
	sort(b,b+n);
	LL dp[maxs] = {};
	LL ans = 0;
	for(int i=0; i<n; i++)
	{
		for(int j=b[i].s; j>=b[i].w; j--)
		{
			dp[j] = max(dp[j], dp[j-b[i].w]+b[i].v);
			ans = max(ans, dp[j]);
		}
	}
	printf("%lld\n",ans);
	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>
using namespace std;
typedef long long LL;
typedef pair<int,int> pii;
typedef pair<int,pii> box;
#define s first
#define w second.first
#define v second.second
#define maxn 1005
#define maxs 20005
int main()
{
	int n;
	scanf("%d",&n);
	box b[maxn];
	for(int i=0; i<n; i++){
		scanf("%d%d%d", &b[i].w, &b[i].s, &b[i].v);
		b[i].s += b[i].w;
	}
	sort(b,b+n);
	LL dp[maxs] = {};
	LL ans = 0;
	for(int i=0; i<n; i++)
	{
		for(int j=b[i].s; j>=b[i].w; j--)
		{
			dp[j] = max(dp[j], dp[j-b[i].w]+b[i].v);
			ans = max(ans, dp[j]);
		}
	}
	printf("%lld\n",ans);
	return 0;
}
```