#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define EPS (1e-10)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

struct st{
	int a,b,c;
};
st p[2000];
ll dp[1001][20001];

int main(){
	int n;scanf("%d",&n);
	rep(i,n){
		scanf("%d%d%d",&p[i].a,&p[i].b,&p[i].c);
	}
	sort(p,p+n,[](st a,st b){return a.a+a.b<b.a+b.b;});
	dp[0][0]=0;
	rep(i,n){
		for(int j=0;j<=20000;j++){
			dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
			if(j<=p[i].b&&j+p[i].a<=20000){
				dp[i+1][j+p[i].a]=max(dp[i+1][j+p[i].a],dp[i][j]+p[i].c);
			}
		}
	}
	cout<<*max_element(dp[n],dp[n]+20001)<<endl;
}
### Prompt

Generate 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>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define EPS (1e-10)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

struct st{
	int a,b,c;
};
st p[2000];
ll dp[1001][20001];

int main(){
	int n;scanf("%d",&n);
	rep(i,n){
		scanf("%d%d%d",&p[i].a,&p[i].b,&p[i].c);
	}
	sort(p,p+n,[](st a,st b){return a.a+a.b<b.a+b.b;});
	dp[0][0]=0;
	rep(i,n){
		for(int j=0;j<=20000;j++){
			dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
			if(j<=p[i].b&&j+p[i].a<=20000){
				dp[i+1][j+p[i].a]=max(dp[i+1][j+p[i].a],dp[i][j]+p[i].c);
			}
		}
	}
	cout<<*max_element(dp[n],dp[n]+20001)<<endl;
}
```