#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
const int MAXN=1024;
const int MAXW=2e4+10;
LL dp[MAXN][MAXW];
struct data{
	int w,s,t;
	LL v;
}a[MAXN];
int n;
LL ans;

bool cmp(data x,data y){
	return x.t<y.t;
}

int main(){
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>a[i].w>>a[i].s>>a[i].v;
		a[i].t=a[i].s+a[i].w;
	}
	
	sort(a+1,a+n+1,cmp);
	
	for(int i=1;i<=n;i++){
		for(int j=0;j<=a[i].t;j++){
			dp[i][j]=dp[i-1][j];
			if(j>=a[i].w){
				dp[i][j]=max(dp[i][j],dp[i-1][j-a[i].w]+a[i].v);
			}
			ans=max(ans,dp[i][j]);
		}
	}
	cout<<ans<<endl;
	return 0;
}
 
### Prompt

Develop a solution in CPP 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;

typedef long long LL;
const int MAXN=1024;
const int MAXW=2e4+10;
LL dp[MAXN][MAXW];
struct data{
	int w,s,t;
	LL v;
}a[MAXN];
int n;
LL ans;

bool cmp(data x,data y){
	return x.t<y.t;
}

int main(){
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>a[i].w>>a[i].s>>a[i].v;
		a[i].t=a[i].s+a[i].w;
	}
	
	sort(a+1,a+n+1,cmp);
	
	for(int i=1;i<=n;i++){
		for(int j=0;j<=a[i].t;j++){
			dp[i][j]=dp[i-1][j];
			if(j>=a[i].w){
				dp[i][j]=max(dp[i][j],dp[i-1][j-a[i].w]+a[i].v);
			}
			ans=max(ans,dp[i][j]);
		}
	}
	cout<<ans<<endl;
	return 0;
}
 
```